Tennessee Williams' version of Chekhov's 'The Seagull'is being performed in Britain for the first time

On 15 February the flamboyant, ageing actress Irina Arkadina will sweep across the stage of the Exeter Northcott Theatre, seducing and bullying her son, Constantin, and her lover, Trigorin. But the actors (Mary Tamm, Philip Cumbus, and James Wallace, respectively) will not be performing in another version of The Seagull. They are appearing in the UK premiere of a play that Tennessee Williams wrote at the end of his life, The Notebook of Trigorin.

Williams called his play an interpretation of Chekhov, but Notebook is something more, an attempt to consummate his love for the playwright by melding his style and themes with those of his favourite play. It was Williams's discovery of Chekhov when he was 24, in 1935, that made him want to become a playwright. At the time, he was recovering from a mental and physical collapse brought on by working, like Tom in The Glass Menagerie, in a St Louis shoe-warehouse. He read Chekhov's plays and letters, and he saw himself in Constantin, the sensitive, talented young man mired in a stultifying provincial town.

But, in years to come, Williams came to feel more of a kinship with Trigorin, the author who is never without a notebook in which the lives of those around him are turned into raw material for his writing. Like Williams, Trigorin is adrift, seeking distraction in sex with younger partners and worried about competition from younger men.

The two main female characters of The Seagull also had much in common with Williams's archetypal woman and girl. Arkadina is similar to his domineering mother, Edwina, full of deluded grandeur, and Nina, whom Constantin loves and whom Trigorin seduces, recalls Williams's fragile sister, Rose, who inspired Laura in The Glass Menagerie and Blanche DuBois in A Streetcar Named Desire.

The Notebook of Trigorin was first performed in 1981, at the University of British Columbia, in Vancouver, where Williams was teaching. Williams was unhappy with that version, and continued rewriting the play until his death, two years later, when it went into limbo. His literary executor, Williams's long-time friend Maria St Just, disapproved of the play. A Russian actress, she revered Chekhov (when she and Williams met, their first conversation was about him), and she regarded Notebook as a desecration.

After St Just died, in 1994, Williams's estate rescinded her ban. The play received its US premiere two years later, at the Cincinnati Playhouse in the Park, with Lynn Redgrave in the role of Arkadina, and has since been performed in regional theatres. Reviews each time have been mixed – one critic found "the sensibility and the language... lovely and lilting and poignant", but another thought that Williams's "demons" had overcome him and Chekhov.

Williams was aware that, in collaborating with the great playwright, he was trying to create a marriage of opposites. "Chekhov," he wrote, "was a quiet and delicate writer whose huge power was always held in restraint. I know that in a way this may disqualify me as 'interpreter' of this first and greatest of modern plays." But, said Williams, "our theatre has to cry out to be heard at all." Indeed, the anguish and scorn, the sexual feelings of Notebook are far more openly and intensely expressed than in the work of the dry Russian doctor, who described his plays as comedies. While the plot remains the same, the characters' motives and personalities have been heightened, sometimes shockingly – it's the difference between a work by a doctor and one by a patient. Williams has cut about half an hour's playing time, trimming the long speeches down to a few lines and eliminating the play's most famous line of all: "I am in mourning for my life."

Ben Crocker, the artistic director of the Northcott, which is fighting for its life in the wake of proposed Arts Council budget cuts, says that, while directing it, he kept in mind Williams's observation that "we are all civilised people, which means that we are all savages at heart."

Williams's resentment of the overbearing woman who demands love but doesn't give it emerges in an Arkadina who, rather than sumptuously self-absorbed, is blatantly exhibitionistic and cruel. When, in this version, Constantin presents his play on a makeshift outdoor stage, Arkadina actually climbs onto it and, declaring that it is dangerous, tries to stop the "worthless" play. Later, while denying her son and brother the money they need to live with dignity ("my son is handsome enough to be attractive in rags"), she prattles about her Paris hat, a necessity for "an actress in my position," and says she would rather appear naked than in costumes that displease her.

One wonders if the harshness with which Williams views her had anything to do with his own dealings with divas, such as Tallulah Bankhead or Bette Davis – the latter insisted, during an out-of-town tryout, that her director not only be fired, but banished from Chicago.

This new, fiercer Arkadina is matched by a Trigorin who bites back. When Arkadina claims that she meant to help Constantin by being truthful, Trigorin retorts, "Since when could you take truth?" He tells everyone that the bottle on her dressing table, labelled "elixir," is actually hair dye. Trigorin's sex life is also more complicated. When Arkadina fears that he will leave her, she tells him that she has come across a love-letter and a sexy photo from a "a long-haired youth," but that his secrets "will remain my secrets... until the day you betray me."

In the Cincinnati production, the identification of Trigorin with Williams was emphasised by giving the actor in the part a white suit and droopy moustache. Crocker is less interested in that aspect than in what he feels is a legitimate addition to Trigorin's personality: "In The Seagull Trigorin is weak and submissive, he doesn't himself understand why he stays with Arkadina. Here he has a more highly developed feminine side, he's bisexual, and she is given a hold on him."

Besides the sex and verbal violence, there's an elegiac, even despairing tone to much of the writing. The lake takes on a greater symbolic weight of death and mystery: "What the lake tells us is what God tells us – we just don't know his language." The most extraordinary change is the ending, which not only goes beyond the point at which Chekhov stopped The Seagull, but alters the nature of its reality, suddenly dissolving the separation between actors and audience.

"It's one of the things that most excited me about the play," says Crocker. "It goes into an entirely different dimension." It is a moment in this story of people who love and destroy one another which sums up what Williams described as his "longing... to bring [Chekhov] more closely, more audibly to you", when we can almost see him reaching out his hand.

Playing to 1 March ( www.exeternorthcott.co.uk)