Among the pile of fan letters Kate Winslet received this week for her performance in the film Enigma, is one that will both delight and puzzle her. It comes from Mavis Batey, an 80-year-old who lives in Bognor Regis, and it ends with a series of incomprehensible words written in capital letters.

"I'm sure she can crack it" says Mavis, who has faith in Winslet as a code-breaker. And when, earlier in the letter, she says she"really identifie" with Winslet in the film, it might be because Mavis was a role model for Winslet's character, Hester Wallace. It was she who told the actress about life among the code-breakers at Bletchley Park.

Batey is full of praise for Winslet's acting."She kept her attractiveness well at bay - though perhaps she slightly overdid the dowdiness" Others, now that the true history of Bletchley in winning the war is finally emerging, are equally full of admiration for Mavis. Without people like her, it might have taken a different course. It was she who cracked the Italian naval code in 1941 and ended Mussolini's plans for treating the Mediterranean as"Mare nostru". She was also instrumental in decrypting the German intelligence messages that led to the success of D-Day.

Even so, when Dougray Scott (who plays the troubled mathematician Jericho in the film) embraced her at last week's premiere and announced:"Without you, I wouldn't be here" She shuddered with embarrassment."It was team work" she protests."I mean, what about all those Battle of Britain pilots"

Describing her work in a new book of essays on the work at Bletchley, Action This Day, she comes across as cool and modest - but razor-sharp. The same is true of her at home, where she sits surrounded by piles of books, about which her husband, Keith - a distinguished mathematician who also worked at Bletchley - teases her constantly.

Mavis was the obvious choice to guide Winslet in Enigma and, early on in the production, she had tea with the producer, the director and Dougray Scott to discuss the project. Keith came, too:"I think they wanted to see what a mathematician looked like" she says.

The Bateys represent the two pincers of the movement that cracked the enemy codes. Keith, who was seconded from Cambridge, favoured the technical approach, while Mavis, a linguist, looked at human elements and word patterns."It is just like driving a car" she says."We can both do it, but Keith understands what goes on under the bonnet"

Their different approaches coloured their reactions to the new film. Keith was upset by factual errors, while Mavis was enchanted by the way it captured the mood of Bletchley and her feeling of being very young and working on something of great importance.

She has some criticisms."I've been doing a lot of Pole-soothing" she says. The Polish role in cracking Enigma was overlooked in the film, she believes, as it is in Robert Harris's novel."It is only
fiction" she tells her Polish friends.

It baffles her that Enigma wasn't made at Bletchley Park itself and she would rather they hadn't shown a traitorous Pole working on code-breaking - which added insult to injury."No Pole worked there, even the great mathematician Rejewski, as it might have revealed the code-breaking centre"

Some details, such as the reward of Scotch whisky for the first to crack the code, also struck discordant notes."In my section, we were never given deadlines - we needed to be calm. Nor was anyone ever singled out. When our work led to the destruction of the Italian fleet at Matapan, we shared two bottles of wine"

In the film, Hester's complaint that women are given only dull jobs didn't ring true with Mavis, either."It looked that way, because the only men at Bletchley were specialists who had been head-hunted. The rest of the staff were women because the men were called up"

Mavis Lever, as she then was, was certainly not underemployed when she went to Bletchley, aged 19. A convent-educated girl from south London with, by her own admission, a very good memory, she was already in the middle of a German degree at University College, London when war broke out. She wanted to be a nurse, but was told to use her German."I rather fancied being a secret agent, seducing Prussians, but neither my German nor my legs were good enough" she jokes, so she went into MI5.

There, she distinguished herself."They were trying to work out where messages were coming from and had decoded one station as STGOCH. Everyone was scratching their heads trying to find the village of St Goch. I looked at the original letters and wondered why we were assuming the capitals were S and G. If you took them to be S and C - it could have been Santiago, Chile"

That display of lateral thinking was sufficient to get her picked for The Cottage at Bletchley, the centre where unbroken codes were tackled. There, she worked under Dillwyn (Dilly) Knox, a classical linguist and interpreter of papyri who had cracked the German naval flag code during the First World War.

"Dilly would be so absorbed in thought that he would stuff his sandwich in his pipe by mistake, and he never found the door when he left the room; he always walked into the cupboard. I was one of Dilly's girls"

On Mavis's first day in The Cottage, Dilly handed her a bunch of encoded Italian naval messages and a pencil and told her to get on with it. Looking at the meaningless letters - which had emerged from the complicated wheels and cross-wires of the Enigma machines - she looked for"crib"; words that might have been encoded. Working backwards, she tried to discover how the machines had been set.

One starting point, she was told, was that messages often began"Pe", meaning"t" in Italian. Mavis had an idea. Perhaps, she thought, the word was"Personal" - personal. Working on that basis, she broke the code soon afterwards, in 1940. And Bletchley were ready when a message came through in March saying that the Italians were planning something big in three days.

Working round the clock, the Allies located the Italian fleet and Admiral Cunningham fooled the Japanese consul (and spy) in Cairo by playing golf on the eve of battle.

As engrossed as she was, Mavis still found time to strike up a romance with Keith Batey, whom she married while at Bletchley - and she dismisses those who say Enigma is inauthentic because, they claim, no one had time for romance.

Together, the Bateys worked on decrypting the messages sent out by the Abwehr, the German intelligence service, which used a more sophisticated version of Enigma."I used the psychological approach. To test the day's settings, the Germans sometimes used their
girlfriends' names and dirty words; it was a great shame when they were stopped, as we enjoyed the dirty words"

When the war was over - two years before it might have been, it is now said, thanks to Bletchley - Mavis and Keith started a family and Keith joined the Civil Service, before becoming treasurer of Christ Church, Oxford. Mavis's new life was"just as much fu" as Bletchley, but habits of cryptanalysis die hard and she produced a series of books decoding the influences on writers including Jane Austen and Lewis Carroll.

She credits Bletchley with giving her a gung ho approach to life."Having been told to crack codes with a pencil and a piece of paper, I was never frightened of having a go" Her only regret is that, having been so diligent when she was young (code-breakers were sworn to 30 years of absolute secrecy), she became highly critical of her own fun-seeking daughters. So it was a relief when the veil was lifted and she could tell them what"silly old square mu" had done during the war.

When she and Kate Winslet met for tea in a Holland Park hotel, there was plenty to say. "I told her about the concerts we went to and the nights at the flicks; the way we swapped clothes to go dancing and the hairdresser who charged 3/6d. We only had a couple of coats and skirts, but always looked smart. We knitted jumpers and dressed them up with pearls and earrings.

"Kate was very anxious about her bump showing in the film as she was pregnant, but she looked fine, if a little scruffy"

Mavis was so convinced by Kate as Hester that she talks about them as one person. Let's hope Kate does have Hester's gift for decoding. If not, she may be chewing her pencil over Mavis's letter for some time. Should she get stuck, Mavis suggests starting with the one-letter word - I or A? - and assuming that the final five-letter word is Mavis. Winslet may also like to know that another word reads"stunnin".

Action this Day edited by Michael Smith and Ralph Erskine (Bantam, pounds 20.99) is available for pounds 17.99, plus pounds 1.99 p&p. To order, please call 0870 155 7222, or write to Telegraph Books Direct, Units 5&6, Industrial Estate, Brecon, Powys LD3 8LA

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