When Hannah Waterman invited one of her friends to come and see her play Beverly, the suburban matriarch at the heart of Mike Leigh's 1977 devised play Abigail's Party, she asked her what they thought of it.

"Oh," came the surprised response. "She's a sexy Beverly."

"I thought she always was," says an equally surprised Waterman in her dressing room in Cambridge on a tour of Lindsay Posner's production which arrives in Edinburgh next week. " She's massively sexually frustrated, which is why she behaves the way she does when she gets drunk, but she's in a very lonely marriage. There's this thread of loneliness that runs throughout the play. They talk about nothing. It's all cars and sofas, but that says so much about who they are.

"I play Beverly as fairly overtly sexual. She doesn't have sex with her husband. She drinks to excess. She doesn't have many friends. Her husband is sniping at her all the time. She's aspirational materially in the way that her husband is aspirational intellectually, but they're both under-achievers, really. People say Beverly's a monster, but it's more subtle than that. She's a really sad character."

Beverly is also something of an icon, and has been ever since Abigail's Party was adapted for BBC television a mere six months after making its stage debut, a speedy transition that would be unthinkable today. As the title suggests, the play is focused on a gathering hosted by Beverly and her estate agent husband Laurence for new neighboursAngela and Tony. Also in attendance is Sue, whose teenage daughter is the Abigail of the title, and who is hosting a far more happening affair next door.

Out of all of this comes a grotesque portrait of upwardly mobile Britain in the 1970s that is the darkest of situation comedies, even as it predicts the materialism of the Thatcher decade it pre-dates.

Developed over months of painstaking improvisation with a cast that included Alison Steadman as an epoch-defining Beverly, Abigail's Party is also a painfully human story.

"It's a play about people's relationships," Waterman observes. "We may laugh at these people, but we all know people like them as well. My mum and I went to a health spa recently, and there were three women by us, all talking in a terribly nouveau fashion about sending their children to private school, and getting things slightly wrong in the way that Beverly does. These are very extreme characters in the play, and you have to recognise that. When we started working on the play, we tried playing it more naturalistically, but it didn't work. It wasn't funny, so you have to try and get the balance, and try to bring these people to life with all their eccentricities.

"We're certainly not trying to imitate the TV version. Alison Steadman was pregnant when she did it, and that made her walk and carry herself in a certain way. I'm a lot smaller, so when the actor who plays Laurence comes at me with a knife, he's a lot bigger than me, so there's a bit more danger, and I hope that brings out a little bit of the vulnerability there is with Beverly."

Vulnerability is something Waterman learnt much about during a four-year stint as the much put-upon Laura Beale in TV soap EastEnders.

"I was 24 when I started on the show," Waterman remembers, "and it was a great place to learn about doing telly. At the time, EastEnders was at its peak, and getting millions of viewers in a way that doesn't happen anywhere now.

"The year before I joined EastEnders was not a good one. I was working in Selfridges selling wigs when I got the call. Being pretty strange looking, I've never really played ingenues. I'm not a pretty actress.

"My mum says I'm lucky to have such a curious face, which is easy for her to say, because she was so beautiful, so I didn't go into the industry with any false impressions."

Waterman's mum is former Royal Shakespeare Company actress Patricia Maynard, while her father is star of Minder and The Sweeney, Dennis Waterman. Watching her parents, Waterman knew she wanted to act from an early age, and joined the National Youth Theatre as soon as she could.

An early stage role cast Maynard and Waterman as mother and daughter in a production of Shelagh Delaney's A Taste of Honey, while Maynard also played Laura's mother in EastEnders. After leaving the programme, Waterman went straight into the west end, followed by stints at the Stephen Joseph Theatre in Scarborough. "I really had to fight my corner," she says of the EastEnders effect, "but doing theatre was like soul food to me."

It was while she was in Scarborough that Waterman worked with Laurie Sansom, who has just been appointed artistic director of the National Theatre of Scotland. That was in Soap, a camped-up satire of TV soap operas in which Waterman proved to be a perfectly post-modern casting choice.

"Laurie is as bright as a button," Waterman says of Sansom, echoing many things that have already been said about him. "He's also brilliant fun, so well done Scotland for grabbing him."

By her own admission, playing Beverly in Abigail's Party is her biggest and most challenging role to date. If things go according to plan, it won't remain that way for long.

SHE says: "I'd like to do a sitcom,. "I've done loads of comedy onstage, but never onscreen, where I usually just stand around looking stern in a trouser suit. I'd also like to do more classical parts. I did a workshop of the old people's Romeo and Juliet with Tom Morris. I played the Nurse, and it was just a pleasure to be around these doyens of classical theatre who were all doing it. I've never done anything with the RSC or the National Theatre, because you have to get your foot in the door, and I've never managed that. I just want to get better at what I do, because I love work. I couldn't not do it."

Abigail's Party, Kings Theatre, Edinburgh, February 25-March 2. www.edtheatres.com