The desk has a typewriter, cigarette ends, a bottle and a photograph of Alfred Hitchcock, the windows reveal views of snowy mountain peaks, and on the walls are wheels of pistols, crossed swords and double-headed axes – cunning instruments of death.

This is the claustrophobic lair of author Patricia Highsmith – creator of charming murderer Tom Ripley, now alone and dying of cancer – and the setting for Switzerland, a chilling, enthralling story about Highsmith, and an examination of the creative process.

A two-hander by the talented Joanna Murray-Smith, the play at the Bath’s Ustinov Theatre concerns the arrival of one Edward Ridgeway, an over-confident, puppyish publishing assistant who has travelled from New York to Switzerland to persuade the curmudgeonly Miss Highsmith to write one last Ripley novel.

From the outset, the author is rude, aggressive, evidently lonely and full of bitterness against a literary world she does not feel a part of. First, she bullies the young man and tries to throw him out – but gradually he wins her over and they strike a deal.

To say more about the plot would certainly spoil it, but suffice to say, even in the opening the clues are carefully placed and the revelation dawns with a satisfying, logical consistency. Highsmith is revealed as an angry racist, an anti-Semite and misanthrope. She rants, swears and makes shocking remarks – yet despite this, does not lose our interest or even our sympathy.

The play explores the way Highsmith lived her own dark impulses through her most famous creation. It considers the motivations for murder, and the way, as readers, we are also complicit when, despite ourselves, we find ourselves hoping cold-hearted, murdering Ripley will get away with his crimes.

The life-size pictures of four Greek maidens on the wall reference Highsmith’s sexuality but also allude to the Muses of myth. The play is speculating about Highsmith’s inspiration, how she created Ripley, where he came from, and by extension, how all writers tap into the darkness to create murderous characters.

Phyllis Logan plays Highsmith. Better known as the good-hearted Mrs Hughes in Downton Abbey, she is almost unrecognisable in the American-accented, inelegant, scruffy-haired, chain-smoking writer. Completely convincing, she gives a terrific performance.

Calum Finlay plays Edward and is more than equal to the challenge. The transformation of his character from bumptious, fair isle sweater-wearing ingenu to – well, what he becomes – is mesmerising. Posture, gesture, voice – all carefully considered, and closely observed. It would be easy for an actor of Logan’s presence and talent to dominate the performance, but it is enthralling to watch the inexorable change in the balance of power.

Switzerland does not you go for a moment. Don’t miss it.

The play runs at the Ustinov till September 1, at 7.45pm, with matinees at 2.30pm on Wednesdays and Saturdays. Tickets are £27.50 with concessions available. A £1.50 booking fee applies. To book, visit theatreroyal.org.uk.