Bringing the story of a waning Brendan Behan's time in the New York to the stage is a challenging task for any dramatist, but even more so for a family member, Janet Behan tells Bernard Adams

As a child Janet Behan, Brendan's niece, was very much aware that Behans made headlines: "Dominic for his songs, my dad Brian for manning the picket lines and addressing the downtrodden masses in Trafalgar Square, Brendan for his wit, his writing and his wayward behaviour."

She also became harshly aware, in a Dublin pub at the tender age of 14, that the Behans had their detractors in the Dublin of the 1950s. She explained: "This bloke turned around to me and said, 'It's the like of these f**king Behans that gives us Irish people a bad name.' "

Now, nearly 50 years after her uncle's death, Janet Behan, actor ( The Beggar's Operaat Druid, panto in Coventry, EastEnders), wife (of television director Dermot Boyd) and mother (of two boys) has taken on the challenge of telling some of Brendan's story. The result is her play Brendan at the Chelsea, which has just premiered in the Riverside Studios in London, and is neatly distanced from both Dublin and London by being set in the Chelsea Hotel, New York, where Brendan was resident for a time in the early 1960s.

There's a nice, modest note about the playwright in the play programme: "Janet has been writing for as long as she can remember, but this play is the first thing she's finished."

Low-key self-deprecation is not a common Behan characteristic, but it's Janet's default mode. There was a standing ovation at the first preview, she tells me, but she's not carried away. Today she's come from her home in Hackney where she has left her younger son Rory revising for his GCSEs, she hopes, and she's feeling bad that her older boy, 19-year-old, severely autistic Finn, is missing out on all the fun because he's away at a special school.

Sitting in the theatrical gloom of the Riverside auditorium, she details the long gestation of the play. "About six years ago I was at home one day, feeling trapped, deprived - all of those things you feel if you're the mother of a disabled child - when someone phoned to ask if I knew anyone who could adapt Brendan Behan's New York for the stage."

The someone she knew turned out to be herself. "The book is a travelogue - which Brendan dictated because his hands would no longer work. So I did a treatment - it was sort of jolly and funny and I used a lot of his short stories." She dared to show it to people and got a clear message that something a bit more dramatic, insightful and hard-hitting was needed, something that wasn't an act of family worship.

"As time went by I thought that if I was going to do justice to Brendan as he was, it had to be warts and all. I had set one scene in the Chelsea Hotel in New York and someone said 'Why not the whole play?' So I did. I knew that at the hotel Brendan was looked after in his room by a troupe of dancers and that he used to hold court and lie there chatting, and not getting on with the book."

Then she thought of focusing on one particular dancer - one who Brendan didn't particularly like and who didn't particularly like him. This promising material was workshopped for three days at the National Theatre. Enter Adrian Dunbar - luckily available, and cast as Brendan for the reading.

"The day after the workshop Adrian came round to my house with a large cake and said he wanted to take the play forward and play the part. This was two years ago. He had a great input and brought many more cakes besides."

Talking to me later the same day, Dunbar takes up the narrative. "I felt that there were areas of Brendan's life that we could explore together. And we stripped out a lot of the monologues until we got the play we have now. I think, by the way, that Janet has a fabulous ear for the Dublin speech of the 50s and 60s because she heard it in her formative years. The whole process had the express intention of making it her play, that we'd have Brendan's voice in it and lots of things Brendan actually said, but that in the end it would be Janet Behan's play.

"You see Janet had started off as an actress and then she gave birth to Finn and that really closed in her life - I became aware of that when I saw how overwhelming having a disabled child can be for a couple. For me one of the big drives behind getting this play finished and onto the stage was the thought it would be a big release for her as a person."

In performance on the first night, Brendan at the Chelseacomes over as lively, if a little fragmented, the acting excellent and the staging awkward. The play shows Brendan failing to surmount various crises: as he drinks more he dictates less; a lover keeps ringing up, threatening to appear at any moment with "his" child; he's short of money; and, most disturbing of all, there's a threat that his wife Beatrice - the wife he has told everybody he is divorcing - will arrive at any moment.

Brendan flails engagingly - singing ("When Irish eyes are bloodshot . . ."), teasing ("You've moved way past happy, you're careering into smug"), gargling with gusto and strewing his bon mots with abandon: "I'm a drinker with a writing problem . . ."; "I didn't turn to drink, drink turned to me . . ." and so on.

Adrian Dunbar makes very little attempt to impersonate Behan, but aims for, and gets, the esprit (his word) and the delivery. But he seems too kempt in the role - the suit not baggy enough, the shirt not grubby enough, the hair too tidy. But he rises to the songs and the witty arias, and suggests that deep down Brendan knows he will not stop pressing the self-destruct button.

Eva Crompton is a lithe and maddening dancer/minder, constantly inflicting the painful details of her groin injury on anyone who would listen. Bríd Brennan comes on late in the play as the wronged but far from downtrodden wife, Beatrice. She stands marvellously still as she realises that his disease and their relationship are in a much worse state than she could have imagined. As they confront each other, Brendan's bitter words brings one or two gasps of horror from the audience; Beatrice movingly says she had no option but to go on loving him.

A problem with this production is that the huge, wide stage at Riverside does not suit it. No designer is credited, and the vital sense of claustrophobia as Brendan confronts his microphone and his problems in his hotel room, is missing. A remix of the whole production, with much better staging and lighting - perhaps in a smaller theatre - would do more justice to a funny, interesting play and some excellent performances.

Brendan at The Chelsea is at the RiverSide Studios, London until Feb 3