Terry Mansfield, managing director of National Magazines, said he was not interviewing anyone else for her job, er, for the moment. Stephen Quinn, publishing director of Vogue at rivals Conde Nast, told the Guardian with damning frankness: 'It strikes me as extraordinary to take someone who has never been particularly successful at anything she has done, and give her a magazine to edit.'
Mr Quinn has since had to eat large quantities of his glossy-paper words. Esquire is still selling below GQ, Conde Nast's parallel general-interest magazine for men, but the gap is closing. The July/August issue of Esquire sold more than 93,000, and growth in the past year is thought to be about 40 per cent.
This year, the British Society of Magazine Editors awarded the never particularly successful Ms Boycott the title of Magazine Editor of the Year for general-interest magazines. 'She's moving forward, and she's really got hold of the market,' says Mr Mansfield.
Ms Boycott is as pleasantly surprised as anyone. When she published her autobiography, A Nice Girl like Me, in 1984, she described her alcoholism, her use of a vibrator and her prison spell in Thailand for trying to smuggle dope into Malaysia, all with such frankness that, she says, 'I thought I'd never be employed again.'
She is willing to make public mistakes to a degree that is either reckless or courageous, or both. After writing her book, she fell off the wagon again when her marriage to the journalist David Leitch broke up. It was easier the second time, she says, to make her way back to sobriety.
A risk-taking personality, however much of a handicap at top girls' public schools, can be useful in an editor. 'You are never remembered for the safe stuff,' as Ms Boycott says. The next issue's fashion pages will feature suits on surf boards: the clothes were all but ruined by the end of the session.
'I'm good at persuading people to do things they don't want to do,' she says. She recently came close to persuading the actress Emma Thompson to appear on the cover nude, smeared in gold paint. It was her idea to start a literary prize for non-fiction, and it was she who persuaded Volvo and Waterstone's to back it. 'She's very energetic, and she fires out ideas all the time,' says an ex-colleague. 'Some of them are loony, of course.'
Her own style is dramatically plainer than that of the usual female editor of a glossy. She wears no visible make-up, and looks discomposed at having to admit that her severely cut trouser suit comes from Armani. 'It's only Emporio Armani,' she says defensively.
Ms Boycott has just asked cosmetic firms not to issue invitations to Esquire for expensive promotional trips. 'We'd never do a fashion shoot in a polo field,' she says.
High-minded as this may sound from a magazine that depends for advertising on such names as Louis Vuitton and Yves Saint Laurent, and whose editorial suggests a pounds 215 teapot as an ideal Christmas present, it is none the less refreshing.
Esquire does, of course, disgust some people, notably Kathy Lette, whose novel Foetal Attraction Ms Boycott condemned on Radio 4's Start the Week. She objected to the book's main character. 'He's a mega-shit. I said to her, I don't meet guys like that. You meet guys who are horribly screwed up. But most guys genuinely want to get on with women.'
Ms Lette responded to her criticism by trashing Esquire as exploitative of women. To my eye, the magazine's current front page, with Kate Moss's gold-covered nipple coyly concealed under a cover line, looks a trifle tacky. But Ms Boycott robustly denies the charge of sexism.
'I liked it,' she says. 'I thought she was proud and tough, saying, here I am, I'm great. I like Naomi Wolf's new book - where she talks about 'victim feminism'. It's time to get on. I think women are very beautiful and can be very sexy, and you just have to celebrate it.'
This is the classic argument for the use of page three pictures. But Ms Boycott's opinions are honestly held. Despite having been the co-founder of Spare Rib, she seems never to have been a hard-line feminist. In 1973, Marsha Rowe, her co-editor, was already accusing her of not being a feminist at all.
When I ask what editing style she prefers in her men's magazine, she says: 'I'm a woman who does this, so you're in a peculiar state of dependency on the goodness and skill of people who work on it - it's a consensus place.' When I repeat her words back to her, she has second thoughts: 'Maybe a peculiar state of dependency is pushing it too far.'
Consensus or not, Esquire now has a reputation as a pleasant workplace and, with pages imbued with its editor's peculiar sense of mischief, it is running some excellent serious pieces, particularly about Ireland (see the present issue's revealing interview with Gerry Adams).
Ms Boycott's last post was as deputy editor of Harpers & Queen. Was that a bit like being back at Cheltenham Ladies'? She nods. 'Esquire is more like a mixed liberal co-ed,' she says.
She is happier than she has ever been. 'I heard about a piece one magazine turned down because someone had written about marijuana,' she says. 'You feel rather despairing. That doesn't happen here. In Harpers, you couldn't have said, 'When I was in prison . . .' whereas here, it feels all right.'