WH Auden is best-known as the craggy-faced genius who wrote such beloved poems as Funeral Blues, with its famous opening: "Stop all the clocks, cut off the telephone,/ Prevent the dog from barking with a juicy bone,/ Silence the pianos and with muffled drum/ Bring out the coffin, let the mourners come."

But for Alan Bennett, the poet was "infuriating" and "a bore" – at least by the time he moved to Christ Church College, Oxford, in 1972, the year before he died.

In an essay for the London Review of Books about his new play, The Habit of Art, which deals with the relationship between Auden and Benjamin Britten, Bennett writes: "Auden somewhere makes the distinction between being boring and being a bore. He was never boring – he was too extraordinary for that – but by the time he came back to live in Oxford he had become a bore."

He must, concludes Bennett, have been a grave disappointment to his Christ Church colleagues. "He was never not teaching and/or showing off how much he knew," writes Bennett. Like Larkin, "he wasn't much fun [...] at the finish" – he was "just infuriating".

Bennett encountered Auden in person while an undergraduate in the 1950s. However, the poet nearly scotched Bennett's literary career.

"When Auden outlined what he took to be the prerequisites of a literary life, or at any rate a life devoted to poetry, I was properly dismayed. Besides favourite books, essential seemed to be a literary landscape (Leeds?), a knowledge of metre and scansion and (this was the clincher) a passion for the Icelandic sagas. If writing meant passing this kind of kit inspection, I'd better forget it."

The Habit of Art, which opens at the National Theatre on 17 November, rests on a fictitious meeting between Auden and Britten in the early 1970s, while Britten was writing his last opera, Death in Venice.

Bennett explains that in order to address the many queries and notes on the text ("do we need this?"; "too much information") from the play's director, Nicholas Hytner, he invented a framing device: the play would be set in a rehearsal room. "Queries about the text could then but put in the mouths of the actors who (along with the audience) could have their questions answered in the course of the rehearsal."

The device also allowed Bennett to introduce the character of the author – himself – who complains about real cuts that Hytner suggested to the play.