People person: Alan Bennett's new play will focus on our need for each other - but it won't be pretty

This week's edition of my local free newspaper, the Camden New Journal, has a picture of Alan Bennett on the front page drawing attention to his public stand on two significant events: the regrettable closure of an organic café, and the celebratory opening of the new Primrose Hill Community Library.

Of course, it was the independence of the café that appealed to Bennett in an age of supermarkets and Starbucks. And the library (to which he's one of 500 named donors) replaces the public one closed by the council in the name of cost-cutting. The café's closure, for Bennett, was a shame; the public library's, shameful.

No one writes more angrily, or acidly, about the steady decline in the "quality of life" for ordinary people in a community and his first new play for three years is likely to continue that campaign in the guise of comic relief.

For People, which opens next week (7 November) at the National Theatre, discusses the pros and cons of sharing one's personal treasures on the open market, setting one's goods free to be shared, in a saleroom here, or an exhibition there. The plot is under wraps, but the central role has been written specifically for Frances de la Tour. One thing's for certain: she won't be singing about people who need people being the happiest people in the world. People who need people in Bennett are usually the old, the lonely, the marginalised, the sexually undernourished, and they often go to church because God might be there; and that includes the vicars.

No, where People is concerned, Bennett is in two minds, probably, on the efficacy of art or the democratic right to enjoy it. Elitism for everyone might be his battle-cry if he wanted one. Which is why he's become such a quietly powerful critic of the closure of libraries, the charging of tuition fees in universities, the "rationalisation" of the NHS, the commodification of public services.

At the end of Forty Years On (1968), his first play, Bennett's headmaster, originally played by John Gielgud, laments the changes in Albion School: "The crowd has found the door into the secret garden. Now they will tear up the flowers by the roots, strip the borders and strew them with paper and broken bottles." The difficulty for Bennett is that the yobs are at the gates as well as the barbarians, and he's really on their side; well, a bit more on their side than he is on that of the management classes, the weasel estate agents in his brilliant adaptation of The Wind in the Willows (1990), bent on developing Toad Hall into executive offices, or the social services in Enjoy (1980), moving the inhabitants of the last back-to-back in Leeds into a museum for the authentic working classes.

It all becomes so complicated, for Bennett wants access for all without dumbing down. His nostalgia for the privileges (or rights) he enjoyed as a grammar school boy is tempered with disgust, rather like John of Gaunt’s in Richard II, that this land of such dear souls, dear for her reputation throughout the world, should be leased out, “like to a tenement or pelting farm.”

The final words in Forty Years On put up the "for sale" notice: "A valuable site at the crossroads of the world. At present on offer to European clients. Outlying portions of the estate already disposed of to sitting tenants. Of some historical and period interest. Some alterations and improvements necessary."

Paradoxically, Bennett himself has become a valuable asset. The biggest success of his career, The History Boys (2004), has made in excess of £5m for the National Theatre, but it struck at the heart of what Bennett is about in its central dispute over the purpose of learning. Politicians discuss the arts in terms of economic benefit. Bennett, like Hector, the defiant English teacher in his play, is with AE Housman: "All knowledge is precious whether or not it serves the slightest human use."

The fact that this brilliant satirist and poet of the heart – a lot of his work, noted Michael Frayn, is about that moment when people wake up to the fact that they have passionate feelings – is a National Theatre institution and not a West End fixture, marks the changing nature of our theatre culture and the increasingly radical tone of his work.

If there ever was any such thing as "a West End play", Bennett never wrote one. But he is, above all, an entertainer, and easily the funniest of all our dramatists. He was slightly miffed to receive a best comedy award in the same year Alan Ayckbourn won in the best play category. He commented wryly on the podium that while his play may not have been better than Ayckbourn's, at least it was funnier.

There's even a strong case for saying that what he writes on the stage isn't strictly drama, but a mixture of revue, vaudeville, farce and sketch comedy. The Madness of George III (1991) is a series of sketches in which more or less nothing happens except for the king passing blue urine. The History Boys is a bit of a ragbag and Bennett himself now admits that Hector couldn't possibly have groped his pupils' genitals while riding a motorbike one-handedly.

And in his last play at the National, The Habit of Art (2009) – People will be his seventh NT show; that's about level with Tom Stoppard, but way behind David Hare, who's had 15 at the last count – he placed a fictional encounter between WH Auden and Benjamin Britten inside a rehearsal room. ("Take off your trousers," Auden ordered his visiting interviewer, mistaking him for a rent boy; "But I'm from the BBC!" protested the media man, as though such things were unheard of inside Broadcasting House…)

The often poignant sexual explicitness, with rough-edged bits, always subversive and unsettling, is often ascribed to a change in Bennett after his mother died. Around the same time, he found he had bowel cancer and came out about his own private relations, first with his house-cleaner, Anne Davies, then with his life partner, Rupert Thomas, the editor of World of Interiors.

His compendium of diaries, profiles, production notes and architectural writing, Untold Stories (2005), is one of the great books of our time, confessional writing at its best, funniest and most purposeful. Once described as a one-man awkward squad, Bennett is nothing if not prickly and morally unforgiving.

But in his fiction, as well as in his stage plays, in masterful stories like The Laying on of Hands (2001) and The Greening of Mrs Donaldson (2010), he writes with an outrageous freedom and underlying compassion that is singular to his temperament: in the first, the hilariously detailed memorial service of a promiscuous masseur becomes a trial and a torment to the Anglican vicar, and a skilful meditation on the church itself; in the second, a widow with a part-time job in a medical school takes in lodgers and joins in their sex games in exchange for their rent.

There are great themes in Bennett: the divided life of spying, the ordinariness of the monarchy, pomposity and stupidity in public life, carnality in the medical and ecclesiastical professions, the loss of dignity, loneliness.

But everything he writes is also an excuse to vent an opinion. And it's because he has so much to say, and can say it so well, that we anticipate the next diary selection in the London Review of Books, or the next play at the National Theatre, with such unbounded pleasure and respect.

'People', National Theatre, London SE1 (020 7452 3000) 7 Nov to 9 Feb 2013