"They're good, they're more than good", she announces with relief. "The New York Times, The New Yorker and another daily one are fabulous. People are congratulating us."
The success of the film, based on Virginia Woolf's novel, is close to Atkins's heart. The idea was born in 1994, when she and her close friend Vanessa Redgrave were playing in New York in Atkins's two-woman play, Vita and Virginia, about the friendship between Woolf and Vita Sackville- West. Redgrave was keen for them to make a film of the piece.
"Without a clue how it could be done, I said to her, `Vanessa, what you should do is get someone to do you a script of Mrs Dalloway', thinking what perfect casting she would be," remembers Atkins. "So she said, `Oh yes, it's a wonderful idea. You do the script.' Vanessa has this gift. She thinks if she decides to believe in you, you can do anything. She's like that with herself. She says yes to everything, and then works out how she'll do it later. So I found myself agreeing to do a script."
After Vita and Virginia, Atkins stayed on in New York for Indiscretions (aka Les Parents Terribles), working on the script during the day. The American television company which originally wanted to back it collapsed, Atkins returned to London after treatment for breast cancer in New York, and her husband, the producer Bill Shepherd, decided to raise the money himself. In July 1996 casting was completed, the director, Marleen Gorris, was in place and the film went before the cameras. Then the money fell through, and Shepherd and Atkins faced financial ruin.
After what Atkins describes as "two-and-a-half horrendous weeks", the producers of Richard III stepped in and raised finance for the film to be completed.
The reason why the adaptation was creatively such a daunting challenge is its complicated three-strand structure, which deals with the middle- aged Clarissa Dalloway and her husband and friends in London in 1923; those same characters as young people, full of hopes and dreams, in 1890; and an apparently unrelated story of a shell-shocked young First World War veteran who commits suicide. Yet the skill of Atkins's writing and Gorris's direction never leaves you in doubt as to who is who or where you are in time.
The other challenge for the screenwriter was to convey the inward fragility of its heroine, in contrast to the apparent poise of her society hostess exterior.
"My first thought when I was re-reading the book and wondering how to do it, was that I was going to have to have voice over," says Atkins. "But British and American audiences do not accept a voice over, whereas Europeans love it. That was my biggest argument with Marleen; Antonia's Line, of course, was full of them. So we compromised, and I made the decision to have only Mrs Dalloway's voice, whereas in the book it's everybody's."
Atkins's fascination with the life and work of Virginia Woolf goes back some three decades, when as a young actress she was asked to play her in a movie which ultimately was never made.
"I was so badly educated, I'd never heard of her. I started with The Waves, which I couldn't get on with; then somebody said, `Try Mrs Dalloway or To the Lighthouse, and I thought they were wonderful. Then I was asked to read extracts from her diaries for a television series called Great Writers, and I was hooked".
About 12 years ago Atkins first started to put together Vita and Virginia, based on the correspondence between the two women, but was unable to get the necessary rights. The director Patrick Garland came to her with his idea for A Room of One's Own, based on Woolf's gently mocking feminist lecture to Girton college, and although she was reluctant to do a one- woman show - she wanted to carry out her Vita and Virginia project - she agreed to read it, for one night only, at the Royal Festival Hall. The show was picked up by Hampstead Theatre and snowballed, with Atkins performing it on and off both here and in the States over the next few years. It also opened the doors to those necessary permissions from the Woolf estate, and in 1993, under Garland's direction, Atkins co-starred with Penelope Wilton in Vita and Virginia in Chichester and London, before she and Redgrave took it to New York.
So what is it that Atkins finds so fascinating about Woolf?
"She gives me huge pleasure. Whereas other people might read something from the Bible every day, I'll read a few pages of Virginia's diaries. The thing she's most known for is being a depressive and committing suicide. But she was also the person most wanted at parties - she was hugely funny - and a lot of people have said I've shown them the humour for the first time. I like her, have grown nearly to love her, whereas she wouldn't like me at all. I'm not educated, I'm not bright; she'd find me boring."
As for Atkins's career as an actress, she is currently giving a highly praised performance as Agnes in Edward Albee's A Delicate Balance - a role she describes as the "engine room" of the play.
"I took the part because I wanted to act with Maggie Smith. At first I loathed Agnes with a passion. She's so rigid, which is really hard to play. But I've grown to like her, or at least have sympathy for her. I'm really looking forward to the next one I'm doing, though, the one I'm learning at the moment. No problem in liking her."
The woman in question is one of only two characters in The Unexpected Man, by Art writer Yasmina Reza, in which Atkins will co-star with Michael Gambon at the Barbican Pit in April. It goes into rehearsal in early March, and opens only four days after A Delicate Balance closes. Which explains why Atkins looks like a woman who has a lot on her plate.
However, there is a lighter side of the actress's work to look forward to, when the film of The Avengers comes out.
"It was such fun. I was up for another part originally, and I said, "Actually the part I really want to play is the old lady with the gun."
The man said to me, "But the script says she's short, she's fat and she has a very sweet face," and I said, "Well, I see no reason why she shouldn't be tall, gaunt and horse-faced" - and they cast me."