“Whilst we always give priority to new plays in our programme, we do stage revivals when there is an imperative to do so,” writes the Hampstead Theatre’s artistic director Anthony Clark in his programme notes for The Best of Friends. So what was the ‘imperative’ behind this revival of Hugh Whitemore’s 1987 three-hander, based on letters George Bernard Shaw wrote to and received from Cambridge academic Sir Sydney Cockerell and Benedictine abbess Dame Laurentia McLachlan?

It’s a polished affair, to be sure, full of eloquent bon mots and spirited epistolary banter, elevated by Patricia Routledge’s dignified presence as Dame Laurentia - “an enclosed nun with an unenclosed mind”. As a piece of theatre, however, it’s as archaic as one of Cockerell’s treasured manuscripts, suggesting the Hampstead Theatre has chosen to celebrate the third birthday of its new building not with a bang, but a wimple.

Taking his cue from his earlier 84 Charing Cross Road, Whitemore has his three protagonists take turns to address each other airily with long excerpts from their written correspondence. Shaw (Roy Dotrice) is playful and jaunty; McLachlan, in contrast, is all dignity and composure. Cockerell, meanwhile - the closest the piece has to a narrator - is a bustling windbag, dropping names ten to the dozen while acting as unofficial go-between for his more illustrious acquaintances.

Isolated incidents resonate: Cockerell’s encounter with Tolstoy in Russia, Shaw’s visit to the Holy Land, a hectic day out in London for Sydney and Laurentia. And one sharp difference of opinion over a blasphemous pamphlet threatens to drive a wedge between the writer and the nun that initially seems insuperable. Ultimately, “the gift and mystery” of friendship endures, Whitemore using his characters’ own words to chart how that friendship deepened and strengthened during their twilight years. References to external events, meanwhile, give some idea of passing time: George VI’s coronation, Stanley Baldwin, a World War Two air raid.

All well and good, but where’s the drama? With the characters digressing on everything from Lawrence of Arabia to Gregorian chant, expectorating witticisms and observations without once conversing like actual human beings, you can’t help feeling this is one for the wireless.

Michael Pennington, the youngest member of the cast by some measure, lacks Gielgud’s lofty presence, while Simon Higlett’s cluttered set only heightens the play’s inherent claustrophobia. More than time separates us from its central trio, whose studied prose stops us getting to know them as flesh-and-blood individuals. In the end it’s like listening in on the most cultured discourse in the world from behind a sheet of bullet-proof glass.

- Neil Smith (reviewed at Hampstead Theatre)