Alan Bennett’s new play People offers the enticing prospect of our National Teddy Bear going head to head with the National Trust. Bennett took over the role of National Teddy Bear on the death of John Betjeman in 1984, while the favourite to succeed him is widely mooted to be Stephen Fry. Essential requirements for the position, instituted by George III, include a good sense of humour, an old tweed jacket and a sharp set of claws hidden away under the fur.

Frances de la Tour is magni­ficent as Dorothy, Lady Stac­poole, in her graceful, fallen dignity. We first encounter her huddling in front of an electric bar fire, wearing a ­vintage (but surely genuine) fur coat, a headscarf and what look like pink pyjama bottoms, although they might be something more intimate. She is dressed this way so as to avoid death by hypothermia, in a state room in the magnificent ruin of a Robert Adam house where she was born and would like to die. The latest in Bennett’s terrific line of lovable mad old bats, she lives with her lifelong companion, Iris (Linda Bassett). Iris spends her time knitting for the soldiers, Dorothy is catching up on the newspapers (she’s just got to 1982), and they enliven their days by occasionally singing and dancing along to Petula Clark’s Downtown. Their gently decaying world is disrupted by the arrival of a twittish, well-upholstered auctioneer, Bevan (Miles Jupp). Bevan also works for a shadowy organisation called the Concern, which buys up places like Stacpoole House for discerning types who want to get away from the masses. PST, he explains: people spoil things. It might make an offer for Stacpoole, but it would want to move it somewhere nicer, such as Wiltshire or Dorset. South Yorkshire isn’t exactly a “must-have location”.

Bevan is one of several characters here who lack nuance, especially if they’re villains, but are still fabulously hateful. The supreme villainess is Dorothy’s embittered younger sister, June (Selina Cadell), the new arch­deacon of Huddersfield. Purse-mouthed, bossy, humourless, she wears a nasty cardigan and stout brogues, and has a close female friend, Guthrie (Guthrie!), who recently swam the Channel. An embittered do-gooder motivated mostly by envy, she dreams of the day when women will “Seize the crosier!” and sell off the no-longer-relevant Winchester Cathedral. She’s also planning a series of “celebrity eucharists” led by figures from business, sport and the world of entertainment.

So, will Lady Stacpoole sell out to the Concern, or will she be persuaded by the National Trust, which sends an enthusiastic ambassador (Nicholas le Prevost), and see her home turned into an immaculate, lifeless museum? Or will she just let it fall to ruin? An unforeseen plot twist, not entirely convincing, leads to a porn film being shot at Stacpoole. There is plenty more rich comedy, though, especially the running joke about the house’s historic collection of chamber pots used by famous visitors — Kipling, Thomas Hardy — their antique pee miraculously un­­evaporated, like the blood of St Janu­arius of Naples.

Bennett says that People was prompted by learning that a fine Methodist church in Bournemouth is now a Tesco, and that, for an audio commentary on Hughenden, Disraeli’s old place, the National Trust has employed Jeffrey Archer, the celebrated novelist, liar, adulterer and perjurer. It has even launched a “phone app” guide to Soho, in central London, to appeal to the younger gene­ration. Ivo Dawnay, of the National Trust, has countered that “the world is very commercial now”, and that Soho is “an area the Trust feels is totally appropriate to explore”. He says that People is elitist. Perhaps Bennett objects to the history of the capital being reduced to the operations of a few powerful families. Dawnay, head of the trust in the capital, is the brother-in-law of Boris Johnson, the mayor of London.

Elitist or not, People gives us masses to think about and plenty of laughs, thanks not least to the reliably ticklesome comic touch of its director, Nicholas Hytner. Bob Crowley also gives us a stunning finale of a set transformation. Bennett’s shrewd observation, allied to his satirical imagination, takes him beyond any boring categories of elitist or populist, left or right. There’s a genuinely thrilling note of scorn here for all our wretched leaders, planners and busybodies. But can any satire keep up with the grotesque realities of must-have-growth, must-have-wind-farms, must-have-4G Britain? Presumably it was after People went into production that we learnt that our “Conservative” government is flogging off Admiralty Arch to a Spanish hotel chain. You couldn’t make it up.

Alan Bennett's latest concoction of groan-inducing jokes parading as a dramatic entertainment People at the Lyttelton Theatre is, in essence, an attack on the whole notion of the National Trust. That's all right with me - it's the manner in which he expresses his message I find irritating. The Trust's representative and a shady double-dealing property dealer are obvious caricatures, with Bennett's contempt for them evident in every line. An archdeaconess in the Anglican church is a horsey lesbian, another Bennett favourite. The plot doesn’t so much thicken as dissolve before the audience's eyes when the second half is almost entirely taken up with the filming of a porn movie on a four-poster bed in the decaying stately home owned by Dorothy Stacpoole and her illegitimate half-sister, Iris. Judging by what passed for porn on stage, it's a DVD that's heading straight for the remainder shop. The movie's director, Mr Theodore, turns out to have had an affair with Dorothy many years earlier so the old girl gets out of her woollies and sensible stockings and changes into the Chanel and Schiaparelli dresses she wore when they were lovers. It's desperately unconvincing, despite the fact that Frances de la Tour does all she can to make the scene credible. Bennett has always been lucky with his actors, and Linda Bassett as Iris is especially fine, bringing to a one-dimensional stereotype a warmth and humanity that transcend the material.

Bennett's two previous offerings - The History Boys and The Habit of Art - were generally well-received. Allow me to express my heretical contempt for the latter, in which two geniuses Benjamin Britten and W H Auden, are depicted as sex-starved or sex-obsessed. Bennett giggles at their inadequacies as human beings - he is much given to giggling these days - while glossing over the demons and angels who inspired their unforgettable music and poetry. Why am I calling myself a heretic? Because Alan Bennett has been honoured with the sobriquet 'national treasure', a term that strikes me as the kiss of death to any creative endeavour. Well, allow me to swear in the cathedral. If anyone else had written People he would have received a rejection slip within days of delivery.

Alan Bennett closes his new play People with his heroine saying: "Let lost be lost. Let gone be gone, and not fetched back." It is a neat way of rounding off Bennett's assault on the National Trust, and on "people" in general.

The play is a lightweight romp through Bennett's familiar fare of ancient institutions, male bottoms, old ladies and thin plot lines. It concerns the fate of a crumbling pile in South Yorkshire, "not a must-have location". Coal was once mined up to the front door. A pit village is on the horizon and the owner's lovechild is in residence. The story is heavy with one-liners, but is lifted by Nicholas Hytner's direction and performances by the superb threesome of Frances de la Tour, Linda Bassett and Selina Cadell.

The vexed property is closely based on Wentworth Woodhouse, the palatial mansion that was the subject of Catherine Bailey's 2007 book, Black Diamonds: the Rise and Fall of an English Dynasty. It now happens to be England's biggest and most problematic house "at risk". Those struggling to save it have troubles enough without the ridicule of metropolitan playwrights. But all is fair in love, war and satire, and Bennett is at least generous in his suite of solutions.

The house in the play has water falling through the roof, its pictures are covered in dust sheets and an ageing chatelaine, Dorothy Stacpoole (De la Tour), sits in a moth-eaten fur coat and gym shoes by a single-bar electric fire. Various survival strategies for the house have failed, including a Japanese golf course, a police college and a cookery school. Dorothy's sister, an archdeacon, is determined to give the house to the National Trust, but Dorothy wants none of it. She is happier for the place to be used for a pornographic movie that supplies a ploddingly risque sub-plot. She is also flirting with an odious auctioneer, Bevan, who panders to her longing for a hot bath and overprices everything. Bevan wants to sell the house to an international syndicate on the basis of moving it lock, stock and barrel to Dorset, one of Bennett's less plausible set-ups.

The National Trust is portrayed as an ogre. Yet it has saved many houses, not only from demolition but from Bennett's various preferred options. When Nikolaus Pevsner visited Welbeck Abbey in 1950, it was used by an army college. The architectural historian mused on whether it would next pass to "the electricity board, the coal board, a lunatic asylum, a convent, school, a sanatorium or a museum?" In fact, it reverted to a private home. Many other houses, such as Chatsworth, Castle Howard, Blenheim and Longleat, also remain in family ownership, albeit open to Dorothy's dreaded public. More than 200 other houses have passed to the Trust.

Bennett is clearly a misanthrope. He writes of public access to great houses with the disdain of a Waugh or Wodehouse. He admits in his introduction to the play to "some authorial sympathy" with the elitism of Bevan, who asks: "What is the worst thing in the world? Other people. P-S-T: People Spoil Things." Dorothy exults: "No people! I like the sound of that."

Where Bennett is on firmer ground is in satirising the Trust's policy of "bringing properties to life", expounded by its representative, Lumsden. Visitors are no longer merely tolerated in the hallowed halls. They are not corralled behind red ropes in reverential silence, their thoughts interrupted by Bennett's "worthy women and occasional men, sitting sentinel in every room, and for what? A cup of tea and a flapjack." Stewards are firmly instructed not to speak to visitors unless asked.

People are now encouraged to use the houses as might a guest, to sit in chairs and read by an open fire, to play the piano, use the billiard room or the croquet lawn, sometimes even to cook in the kitchen. They can compose poetry at Coleridge's desk and sit under Newton's apple tree. They can play TE Lawrence's records at Clouds Hill, or paint their own Gainsborough portrait at Beningbrough. While such access and experiences may seem ersatz to the gilded of Primrose Hill, the enjoyment is real and hardly merits contempt. Not everyone can visit Penshurst or the National Gallery or Fountains Abbey "out of hours", as Bennett's programme note implies he is able to do.

Nor is everyone blessed with a Courtauld degree and a mental catalogue of English artists and craftsmen. For many people, visiting an old house is a puzzling introduction to an alien world; a voluntary, paid-for act of self-education. They appreciate being helped across the barrier dividing modern audiences from England's aesthetic and social history. Tourism is the most extensive adult education in the land. I cannot see the virtue in deploring it.

Bennett raises, but does not answer, the question of what the "message" of these places should be; where they sit in the nation's inheritance. Stacpoole house is in a queue that includes "the childhood home of Cilla Black, the pithead baths at Featherston, and the last children's library in the north-east". The Trust is even awaiting receipt of a "dirty protest" cell in the Maze prison. It is true: heritage has moved on from high art, but to where?

As the Trust's Lumsden explains, gone are the days of "aspic … red ropes … Do Not Touch signs … everything in its place". Upstairs, Downstairs and Downton Abbey have resulted in "the scullery and the still room being as important as the drawing room". Lumsden exults over the discovery of a cupboard of chamber pots, in which is preserved the urine of Kipling, Shaw, Hardy and Asquith. "We cannot halt time," he says, "but we can put it on hold … I can almost smell it." Even Dorothy is told that she should remain in situ, a human metaphor of English history in all her moth-eaten glory, "enthroned among your treasures". She is "part of the story" even if, as she admits, "South Yorkshire is not conducive to anecdote".

This is all a hilarious spoof on the Trust's efforts to make houses seem less like mausoleums. But the challenges are real, and Bennett's critical standpoint obscure. He derides the "stabilisation of decay" involved in not replacing tatty furnishings, "gnawed by mice and wet by generations of dogs". He derides the political correctness of chopping down trees to reveal the pit cottages across the park. But what is to be done? The march of decay can easily take over, degenerating old buildings and landscapes into Ozymandian "trunkless legs of stone" in a George Osborne business park. Conserving them involves endless choices.

Do you open the curtains at Hardwick and risk damage to the ancient tapestries? Do you reinstate an interior after a fire, as at Uppark, or leave it scorched and empty, as at Seaton Delaval? Do you replicate half an Axminster at Kingston Lacy so people can walk on it, or leave the old one intact and roped off? Should the Tudor garden at Lyveden be reinstated, as at English Heritage's Kenilworth, or left a ghostly mound in a field? Should cycling enthusiasts be allowed to ride penny farthings at Snowshill, even if a few get battered in the process?

Bennett claims to feel a "sense of unease" when he enters a grand house, at being "required to buy into the role of reverential visitor". That is why the Trust is trying to change him from reluctant worshipper to welcome guest. Since every house is different, guests react differently. Some wish simply to admire the art and architecture. Most, nowadays, are more intrigued by how houses worked, by what it might have been like to live in them, by the stories of the families who occupied and sometimes still occupy them. There is undeniably something prurient, even voyeuristic, about peering around someone else's home. The door marked private is always the most exciting. But conservation is fascinating precisely because there are no clear answers to these questions.

Bennett supplies none. But two principles should guide decisions. The first is never to destroy those few physical remnants of the past – landscape and buildings – that we are lucky enough to inherit. The second is that, where these remnants have been given to the nation and supported by the public, that public has a right of access. Access not as devotees in a heritage cathedral but, insofar as is possible, as day-to-day users.

I assume Bennett does not sneer at the audiences for his plays. He even purports to "interpret" them, in radio interviews and his play introductions. Why ridicule the Trust's public? Perhaps he deserves the torture of Prometheus. He should be acquired by the nation and put on public view, while adoring old ladies dust his eyebrows and explain him to passing tourists. He should be bequeathed to the National Trust before he is past saving.