As muses go, a homeless septuagenarian with a penchant for emotional blackmail and relieving herself in plastic bags (which she proceeds to hoard like precious heirlooms) is quite a bizarre choice. And for close to two decades Alan Bennett himself wavered.

Should he leave his accidental squatter Miss Shepherd well alone, or commit to paper the baffling force of nature’s divagations and daily fixations? She was, after all, a ready-made character.

This inner struggle rears its head again and again in the The Lady in the Van; though, of course, as the title suggests he did, in the end, cave.

Bennett’s acquaintance with the feisty Miss Shepherd began with a typically thankless favour. She wanted her van moved down the street to a new berth. Bennett obliged. Before long the enigmatic and foul-smelling Miss Shepherd had installed herself permanently in his garden – to his neighbours’ great relief – where she would remain for 15 years; roping him in as her reluctant carer.

The genuinely eccentric Miss Shepherd (which may or may not be her name – she is evasive on the matter) used to drive ambulances in the war, has an unexplained aversion to piano music, may have been a nun, and is described by Bennett as “a bigoted, blinkered, cantankerous, devious, unforgiving, self-centred, rank, rude, car-mad cow”.

As the true story of their rather one-sided relationship unfolds, the playwright recalls with humour and self-derision their flare-ups and his strange arm’s-length routine with the woman who so thoroughly insinuated herself into his life.

Sam Alexander and James Northcote make a sharp and merry double-act as Alan Bennett’s split personalities; one forever sitting at his desk, issuing barbed remarks to his timid alter ego who never quite seems to know what to do with the fearsome Miss Shepherd (who is sympathetically brought to life by Sara Kestelman).

The perfect balance of obnoxious and incorrigibly self-centred, Kestelman still manages to imbue the old woman with surprising grace and vulnerability; painting a nuanced portrait of a complex and increasingly frail character. Supremely witty, Bennett’s colourful homage to his accidental neighbour is as heart-warming and entertaining as ever. I, for one, was moved to tears.

The Lady in the Van runs at the Theatre Royal Bath until September 2.