But there's one fantasy that we know Johnson has never entertained. It's the one in which she is asked to write a play shaped around the songbook of a 1970s pop group. Other writers have already tried and failed, but when she meets the two songwriting members of the band, they OK her treatment, and after two years on the project the show opens in the West End to near unanimous and unstinting applause. In this fantasy, she will have journeyed in one playwriting decade from living on family credit to a moment when, some time early next year, it is predicted that she will become a millionaire.
The thing about Johnson's involvement in Mamma Mia! is that it's not a fantasy but a reality in which she still struggles to believe, even with its cast appearing before 100,000 at last Sunday's Party in the Park concert in London. "I'm still not confident that it's going to go on," she says. "It is, though. It's just me. I won't believe it until it's been running for about five years. I suppose I'll always be panicking that it will close tomorrow." When she says that "my children have taken to my new-found wealth with great ease", the implication is that she hasn't.
Nor would her muse want to. Johnson's is the kind of success that could only grow out of the fertile bed of, if not quite failure, then certainly a circumscribed life of unfulfilment, of getting it wrong and muddling through. She writes with gnawing honesty and searing wit about womanhood. She is also almost classically bawdy. The only thing that might undermine the immediacy of her voice is the distance that wealth will put between her and the lives she describes. Although her dramas often fix on the co-ordinate of a rite of passage - getting married (Mamma Mia!), turning 40 (Shang-A-Lang), clambering up a mountain on a spiritual quest (Dead Sheep) - the life-changing addition of a number of noughts to her bank balance will not, you suspect, form the basis of a future play. It's just not real enough.
She certainly doesn't seem the type to change her spots. We met at the Bush theatre, where she has had three plays mounted. She is nursing a grand hangover, and the ashtrays and empties (but not the needles) littered onstage are a familiar sight from an almighty night before.
She talks with an accent that is vaguely Bristolian, although she also spent much of her youth in Cornwall. She left school at 16, a day or two earlier than planned: celebrating the completion of her O-levels by wearing a halterneck top, she was expelled. I ask her if she regrets not pursuing her education (her father worked for the Workers' Educational Association). "Only in that I sometimes feel a bit thick. But I probably would not have started writing, or I wouldn't have written about the people I write about, or written the way I write."
She spent her 20s "in a haze, chilling". She worked in Debenhams, pubs, an accounts office, a record shop. "I was unfocused, I guess. But it didn't seem to matter, because I thought as soon as I want to I'll pull myself together." She told herself that she would one day become a playwright, an ambition first formed at 12 when she wrote, directed and starred in a class play in which she also cast her brother as a non-speaking dog. But by the time her 20s ended she was a mother and living on welfare. "I had been drifting along all my life going, `I'll be a writer one day.' And then one day happened and I thought I'd better do something. It wasn't that I thought I could. I didn't think I could do anything else."
She entered a play called Rag Doll, "a happy family play about child abuse, incest and sausages", in a competition run by the Bristol Old Vic and HTV, and for a while didn't open the envelope announcing her victory, assuming it was another bill. The prize, apart from a bit of pin money and an eventual performance, was a masterclass with Terry Johnson, whose major credit at that point was Insignificance, a forbidding play about the theory of relativity. "I thought he was going to be very intellectual and perhaps a bit unapproachable. I thought he was going to lecture. His masterclass has stood me in such good stead over the years. He told me very basic things. You don't go telling the audience everything. You find other ways of showing them. I love it in writing where you know that so much is going on underneath what people say. I get really bored with plays where everybody is incredibly articulate and can talk about themselves."
Aside from theatre, there were a couple of gigs for the BBC - Sinbin, starring Pete Postlethwaite in a hospital for the criminally insane, and half a dozen episodes of Love Hurts, the middle-aged romance starring Adam Faith. These allowed her to join the mortgaged classes and discover whole new vistas of debt. Mamma Mia! came in early 1997 thanks to a word from Terry Johnson. The producer Judy Craymer, who had worked with Bjorn Ulvaeus and Benny Andersson of Abba on Chess, was looking for a writer to sew the Abba songbook into a seamless narrative. Johnson recommended Johnson. "I talked about my idea with Judy. My treatment was sent to Bjorn and then he asked for a meeting. That was scary to start with. He talked about the plot and it suddenly felt, this thing is going to happen. We all got on. Bjorn and Benny have both got a very good sense of humour. I'd always been slightly worried they might not get the jokes, but then, let's face it, you have to be very obtuse not to get my jokes. They are rather larded on."
It's only the scale of execution which separates Mamma Mia! from Shang- A-Lang, Johnson's play about a trio of women who mourn the passing of their 30s with a weekend of hellraising at a Bay City Rollers weekend. Written in tandem, they both play on 1970s nostalgia, and share her favourite motif of the three-sisters-in-arms. The three middle-aged gal pals in Mamma Mia! are a former girl group, Donna and the Dynamos (Johnson would like to do a Rock Follies-style television spin-off ). Shang-a-Lang is a rather darker exploration of the meaning of friendship, and in Love in the 21st Century Johnson puts that friendship to the ultimate test.
The six half-hour films are designed to reassess the basic tenets of female amatory behaviour. The idea was pitched to Channel 4 by Nicola Shindler, the producer of Hillsborough and Queer as Folk, and Johnson, who wrote three of them: Fantasies is one, Toyboys another, about a teacher in her 30s who has an affair with a 15-year-old pupil. But her initial idea, on the train up to London to make the pitch, was Threesomes, about a woman who sleeps with her best friend's man.
"Often in drama women get portrayed as rather wonderful. They are always so bloody understanding. They always get it right. Men tend to write women a bit like that. Men are always written as these really rounded characters who do nasty things."
I suggest that this may be a roundabout way for male writers to lionise their own gender: self-admiration in the form of self-loathing. Johnson has devoted herself to paying women the compliment of fleshing them out. "I wanted to do it for the girls," she says. "Warts and all."
`Love in the 21st Century' begins on Channel 4 on 21 July. A production of `Shang-a-Lang' begins a national tour from 2 September in Northampton