Hark] The girls of Chelmsford sing: They're brilliant at passing exams, but how do Mrs McCabe's league-table toppers chill out at the end of a long, hard term?

In the last week before the Christmas holiday a second-year class at Chelmsford County High School for Girls in Essex was relaxing with a quiz, a tortuous letter square in which 20 Latin words were concealed. No more than 10 minutes into the lesson a girl at the front announced she had completed her task. 'Oh, are we supposed to say when we've finished?' said another 12-year-old. 'I finished ages ago.'

By every measure, Chelmsford High is the most academically successful state school in the country. Every time the Department of Education's exam league tables are published, for GCSE, A-level and university admissions, there it is at the top. This is the school the Tory press loves, the opted-out, self-governing, selective-entry lesson to us all.

The day she arrived as headmistress at Chelmsford three years ago, Bernice McCabe started to cut items about the school from the papers. It seems from her collection that the gender of the school's pupils combined with its geography is a cocktail that headline writers can't resist. The walls of her office are littered with shrieking double entendres: 'Essex girls come first'; 'Essex girls on top again'; 'It's official: Essex girls have the best p-asses.'

The chance of meeting the air-headed stereotype of Essex gags in the classrooms of Chelmsford, though, is about as high as spotting Julian Clary at a function at 11 Downing Street. Of the 1,000 girls who sit Essex county's 11-plus exam every year hoping for admission to the school, only 93 are selected. With seeding like that it is little wonder the place hums with academic achievement: 98 per cent of the girls attain 11 GCSE A-C passes; 95 per cent go on to university; more than 15 per cent win places at Oxford or Cambridge. Girls come from all over the county to study there; one girl leaves home in London at 6am to arrive on time.

Mrs McCabe was significantly less triumphant about all this than her press publicists, however. 'The reason I started collecting the cuttings was to alert the girls to the fact that what they were achieving was of national significance,' she said. 'But I do feel uncomfortable about exam tables because they don't really reflect what's going on here.

'We are, after all, highly selective, you would expect us to do well academically. But so much more goes into the girls' education. I believe there is absolutely no point in having a school that gets good exam results if the pupils are miserable. I want this to be a place where they believe they can have fun.'

At the final assembly of term, as she sat on the platform in the school hall, the ranks of her pupils stretching out before her, Mrs McCabe did not mention the word exam once.

'Morning girls,' she said as she stood up after the school orchestra had performed a note-perfect selection from Phil Spector's Christmas Album. 'Morning Mrs McCabe,' they replied in unison.

The assembly turned out to be a procession of girls going up to shake hands with the headmistress and be cheered by their peers. They came up in their dozens; girls in the lower years in their compulsory uniform of grey skirt, white shirt, blazer and tie; sixth-form girls, who can wear what they like, but in practice adopt a uniform of ankle-length flowery skirts, Doc Martens and hair which needs to be constantly pulled away from the face by running a hand through the fringe while, at the same time, flicking the head backwards.

There were awards for class 7E, which raised more than pounds 350 by staging a sponsored silence, for the house which won the debating competition, for the girl who had organised concerts in the local hospice. The strongest applause was for the winners of the best-decorated classroom on a Christmas theme.

'Their splendid efforts deserve to be announced in full assembly where they will receive most publicity,' said Mrs McCabe, declaring, to cheers, that the contest had been won by 7C, who had decked their room out in holly and ivy.

My vote, however, would have gone to the class who had transformed their place of work into the insides of Father Christmas, an offering that was on show to interested observers after the assembly. From the ceiling hung cardboard organs, bones were pasted on to the blinds, girls dressed in red or white T-shirts danced at the tables with labels round their necks saying 'corpuscle'. Suddenly, to much shrieking and giggling, a girl in black ran into the room and attacked the corpuscles with a cardboard tube. She was playing a germ. Meanwhile, two girls sat inside a cupboard, rhythmically hammering the door to represent the heartbeat.

Everything appears to be done at speed and in competition, even in the gym where girls in navy knickers and handicapped by considerable puppy fat perform quick routines they had choreographed themselves in less than a week. According to Mrs McCabe, the girls have 'a voracious capacity for information' which often catches new staff unawares - they prepare lessons for what they think will last a term and run out after three weeks. Such ability to learn quickly generates an impressive self-confidence in the pupils.

Though the Tory papers gush about this embodiment of the success of government philosophy, the girls' own politics appear overwhelmingly liberal. Those I met may have been ambitious and career-minded, but they were also concerned in a 'Prince of Wales something-must-be-done' sort of way. They raise stacks of money for charity (usually for animals), organise themselves into committees to supervise recycling, and worry about the environment.

The only real sense of conservatism is that, like most schoolchildren, they love their traditions ('A forward-looking girls' grammar school that retains a strong belief in traditional values' is the school motto, decided on by the girls themselves). At the annual carol service in Chelmsford Cathedral, the girls insist on things old-fashioned. No calypsos, reggae or raps, just seven carols and seven lessons, superbly sung and wonderfully read.

Mrs McCabe's aim, she says, is to push her pupils both academically and in areas outside the curriculum; to prepare girls for their role as women in the modern world, juggling careers and families.

Like Mrs McCabe, in fact, the very modern headmistress. She is studying for an MBA, which she will complete next summer at the University of Southern California, and has, now the school controls its own budget, negotiated a performance-related pay clause in her contract. She drives an Astra GTE, wears elegantly tailored suits and has her hair power-bobbed in the style favoured by women in advertising or the City. We are not talking blue-stocking here.

Oddly, despite the role model, few of Mrs McCabe's pupils become teachers. In the group of five sixth-formers I met, two wanted to be lawyers, one a doctor and two journalists. 'None of the girls ever says they want to be a teacher,' said their form tutor. 'They're far too ambitious to admit anything like that.'

(Photographs omitted)