For someone so mock modest about himself, Alan Bennett is increasingly exhibitionist these days, writing not only about his illness, sexuality and parents, but even authorising this latest vanity project at the National Theatre in which Alex Jennings gives an absolutely wonderful pitch perfect performance in his stead.

You gasp when Jennings first appears in that familiar Brooks Brothers regulation dress code of grey sports jacket, comfortable trousers and shoes, the blue short-sleeve sweater, the red tie (replaced with a turquoise one for the second play).

Bennett himself appeared on the National’s stage as Sir Anthony Blunt in his A Question of Attribution play about one of the Queen’s pictures. Otherwise, in the West End, he’s been impersonated, or embodied, by Nicholas Farrell and Kevin R McNally as his public and reflective selves in The Lady in the Van.

But only Jennings has added the exact sly, deferential physicality of Bennett to his portrait, the inquisitive gleam in the eye, the crook of the head, the slightly open-mouthed gawp of disbelief, the unlikely blond schoolboy haircut, the slim tallness of him.

Hymn, directed by Nadia Fall, first seen (with Bennett playing himself) at the Harrogate International Festival in 2001, is a half-hour patchwork of his school, church and concert-going musical memories, with some beautifully evocative music by George Fenton played by a string quartet.

Here are the touching accounts of concerts in Leeds Town Hall that we’ve relished in his diaries, the clever descriptive distinction between two demonstrative conductors, Sir John Barbirolli and Sir Malcolm (“Flash Harry”) Sargent, the disappointment he feels he caused in his father by not emulating his proficiency on the violin.

There’s a J B Priestley link in the two pieces, as the first contains an account of a visit to the 16th century church in Hubberholme where Priestley’s ashes are kept (I once visited the church during the Harvest Festival after a long walk that gave the outing a sense of pilgrimage); and in the second, Priestley pops up telling AB that you never saw Proust on roller-skates and that literature can be about anything or even nothing: “Look at bloody Samuel Beckett.”

Cocktail Sticks, directed by Nicholas Hytner, is the richer text as AB measures his life against the lower middle-class expectations of his parents, beautifully played by Jeff Rawle and Gabrielle Lloyd. He discovers some unused cocktail sticks in Mam’s kitchen cupboard; she chides him for not giving cocktail parties at Oxford, as Beverly Nichols did.

Party food for his parents meant Shippam’s fish paste. And AB’s cocktail comes, these days, not in a shallow glass, but in a bag, “a transparent udder that drips toxicants (though not intoxicants)” during his two-day binges every fortnight. But all that was fifteen years ago. And Jennings bows his head at his desk and starts typing.