Outside the ranks of journalists, few people have heard of Tina Brown. In New York my taxi-driver hadn't, nor the woman who checked-in baggage at JFK airport. In England, an academic friend said 'Why talk to her?'

Why? Because Tina Brown is the queen of New York and whatever that may mean it has to be an accolade for an Englishwoman who is not yet 40. Because she has made first Vanity Fair and now the New Yorker compulsive reading in a country with thousands of magazines. During her eight years as editor of Vanity Fair its circulation quadrupled. Within a year, she has boosted the New Yorker's circulation by 130,000. In professional circles, she is known as the most formidable editor in the world.

The first impression is daunting. Her glamour is instantly apparent, but so is the legendary ruthlessness. She shakes hands in her sleek office unsmilingly and accepts a present smoothly, unsurprised. She is slim and impeccably dressed in a dark navy suit, her hair cropped short and her face lightly tanned. She has wide-open eyes, long eyelashes, and an intimidating manner. She doesn't blink, she doesn't fiddle, she has no nervous tics, she just concentrates.

Tina Brown has been a phenomenon ever since she went up to Oxford to read English. She came from a comfortable background, somewhere between the Home Counties (her parents had houses in Marlow and Marbella) and film worlds (her father was a producer).

A tutor recalls: 'Here was this incredible child who, at 17 or 18, was living like a 30-year-old. Not your average kid of that age, especially in the early Seventies, she was very sophisticated: flamboyantly and ostentatiously so.'

A friend from Oxford recalls: 'She had undergraduate parties and invited Martin Walker from the Guardian and he came. Martin Amis and Craig Raine were friends. She had a very precise instinct about power and what use it was. Naturally she gravitated to people who had it. She was almost navely frank about her ambitious nature.'

The emotion she evokes today is extraordinary, amounting sometimes to paranoia. One former staffer at Vanity Fair burbled away happily until he realised that I wanted to quote him, when he became seized with terror. His remarks were anodyne enough: 'She echoes the prevailing mood and knows how to keep in with the in-crowd . . . she changes with the wind and can jump instantly to the latest intellectual fashion'. I promised anonymity, but he implored me not to use his more vituperative comments. Ten minutes later he rang back and implored me not to use anything at all. Ten minutes after that a colleague rang on his behalf and pleaded with me as well. 'Ms Lambert, X begs you not to quote him.'

Tina is a power not to be underestimated; she always has been. She has stage-managed her career and reputation quite brilliantly, and knows exactly how to exploit publicity. From Oxford, the university magazine Isis, and some writing for the New Statesman, she joined the Sunday Times. Her first play won the Sunday Times Drama Award in 1973 and she was voted most promising journalist that same year. At the age of 25 she became editor of Tatler, in June 1979. There she debunked the new 'flash-trash' with the same glee as she dismissed the old aristos and Tatler's circulation trebled.

From across the Atlantic, she attracted the attention of S I ('Si') Newhouse, the ninth richest man in America and owner of hundreds of local newspapers, leading publishing houses (including Simon & Schuster and Random House) and the magazine giant Conde Nast. In 1982 he bought Vanity Fair for Conde Nast and in 1984 he brought Tina Brown to New York to rescue it from the doldrums.

She arrived with her new husband Harold Evans, former editor of the Times and Sunday Times. Within 18 months, in the teeth of bitter hostility from New Yorkers, Tina had turned the magazine around and by the time she left, after nearly eight years as editor, Vanity Fair's circulation had risen from 220,000 to nearly a million. People might deplore its new vulgarity and many did, but they read it. Tina had conquered.

Meanwhile the venerable New Yorker, founded 68 years ago, was foundering. By 1985, when the Newhouse family added it to the Conde Nast stable, it had become an old man's magazine, its readers' average age close to 60. William Shawn, its 77-year-old editor was replaced by Bob Gottlieb, but in June 1992 Si Newhouse dismissed Gottlieb and turned - not surprisingly - to Tina Brown.

The move was sudden and highly criticised. The New Yorker is a venerable institution, cherished by more people than actually read it. Plenty wanted to see Tina fail. She has not. She has a rare ability to give her entire attention to the current problem. Last summer, that problem was revitalising the New Yorker.

'I basically redesigned the magazine in my house on Long Island over three months and then came in and implemented it. I have a great sense of mission about making the New Yorker work. I don't want to be pompous about it, but a lot of trust has been reposed in me not to let standards go. My critics are longing to pick up the magazine and find a pregnant Demi Moore on the cover and it won't happen.' Everyone who knows her says that she is the most focused person they've ever met. Is it true?

'At 20 I was very focused on getting my play done - getting it good and getting it on - I turn from one thing to the next and I work very hard and I think about it all the time: isn't that what everyone does? In order to sustain a job like mine and make it work you've got to be tremendously focused. I don't have much leisure. I think about the magazine all the time, 24 hours a day, in the car, in the bath: all the time. It's a very fascinating and consuming and rewarding job. I love my job. I love my life.'

What is a normal daily routine?

'I get up at 5.45 and go to the gym at the end of the street for an hour. I never used to do that, but I really find it gets me through the day and gives me energy. Then I have my shower, wake my children up, walk Isabel (her three-year old daughter) to the International Free school and come to work. I try not to leave work after 5.30, and then, between 6 and 9pm it's bedlam with the children. Finally George (her 6 1/2 -year-old son) goes to bed and then it's like the Elves and the Shoemaker, because I do a lot of work in the evenings at home: the faxes begin, and it's another sort of bedlam. I sleep less than six hours a night which I truly don't like, but I need that little to spend any time with my children. The gym is my safety-valve. But my predicament is that of every working mother. I work no harder than a lot of ladies who don't have my rewards or my satisfactions.'

Nobody knows exactly how much Tina earns but it is rumoured to be dollars 500,000 ( pounds 325,000) a year, basic. She has brought her parents over from England to live next- door to her Sutton Place apartment. One of the smartest addresses in New York, in the south of Manhattan, it has water and sky and a wonderful view. But she is homesick for England, and would prefer to educate her children here.

'I do miss England - the irony and humour most of all; I miss the lack of humbug. I love the culture of England. You tend to idealise a place you left nearly 10 years ago, but I miss the beauty of London, which hits me every time I go back. I have many funny, smart friends there whom I miss a lot. I miss the summer, the winding lanes of the English countryside, and I miss the month of June. I miss the great newspapers in England: the ones here are terrible. I miss the whole way of life. England is a much nicer place to bring up children than New York, but I do love working in New York.'

New York, perhaps sensing this innate Englishness, has been pretty intolerant of her. Since she took over the New Yorker it has been called glitzy and trashy. People claim she has sold out the high standards entrusted to her.

'The people who criticise me are not reading the magazine. They say, oh, I so miss the New Yorker the way it was: the 100,000 words on zinc or the thousand words about the apple-vendor. I tell you, those people didn't read it then and they don't read it now. The New Yorker has always been an evolving, changing magazine. I'm using the same writers - Updike, Janet Malcolm - and I've added some new ones. I've tried to make the wonderful articles that were always there accessible. News-stand sales - always the most important barometer for success - have gone up from 15,000 to 60,000.'

I read four recent copies of the magazine during my flight, and was surprised by their excellence and variety. Articles are long, analysis is often profound. The cartoons are as incomprehensible as ever. One very obvious difference is the flood of new advertising: scent, fashion and cosmetics that, I said, would look more at home in Vanity Fair. She counter-attacked at once.

'I understand my business: that if you don't get the advertising, you get fired. If you don't deliver, you're gone. There's a revolving door at Conde Nast. Our advertising is 26 per cent up and to say it's heavily discounted (the charge levelled at her by critics) is just a lie. It's unheard-of for us to have 101 pages of advertising - better than I ever dreamed.'

She will be 40 next month. Is that a milestone? She pulls a face. She hardly ever grimaces, and her skin is still almost unlined.

'It's a millstone. It's not that important to me. My face will probably collapse like Cinderella but I don't care. I have two children I adore and a husband I, er, adore' (the hesitation, I sensed, was because she feared sounding mawkish rather than because she didn't mean it) 'and a wonderful job and I wouldn't change it. I love it all.'

It had been a tough, combative interview. For two hours she didn't smile or soften once. She is the most implacable person I have ever talked to, and I can see why she is at the pinnacle of her profession.

Maurie Perl, the New Yorker's PR director, invited me to lunch afterwards at a restaurant opposite the New Yorker offices. At the end of the meal, Tina Brown stalked unsmiling past our table. She didn't even flutter her fingers in acknowledgement, to either of us.

This is the last in Angela Lambert's series of interviews; Hunter Davies returns next week.

(Photographs omitted)