‘So were you levitating with rage by the end?’ I asked her. She — a veteran of Bletchley Park — and I were discussing The Imitation Game, the new film about the mathematician and code–breaker Alan Turing, featuring Benedict Cumberbatch and a host of historical inaccuracies. But she remained sanguine: ‘Not at all, I really enjoyed it a lot. A little dramatic licence here and there, but that’s what you get with films.’

Indeed. Still, the film didn’t take the biggest dramatic liberty of them all, thank goodness — that of suggesting that Bletchley’s triumphs were entirely down to the Americans. This claim — blood still boils at the mere memory — was famously made in the Hollywood blockbuster U-571, which depicted the Americans grabbing a German Enigma code machine off a U-boat and thus saving the world. They didn’t. The Enigma snatch was down to three astoundingly brave British sailors, two of whom died during the raid, and whose sacrifice helped Britain survive the Battle of the Atlantic.

Thankfully, the U-571 version of events is no longer orthodoxy in the States. When I was there recently, giving a series of lectures on the subject, I found to my surprise that people were eager to hear the story of a quintessentially British victory — the cracking of all Nazi ciphers, including messages from Hitler himself — in this most secret wartime establishment in a leafy corner of Buckinghamshire.

On a train between New York and Philadelphia, for instance, I got talking to a lady who, on hearing of my interest, became absurdly animated and called her husband on her mobile. There then followed from both of them a friendly barrage of Enigma questions, broadcast to the entire carriage.

Some of those whom I met at my talks told me that the code-breakers’ story encapsulated what they considered to be the finest of English attributes. These citizens of Los Angeles and Boston were devotees of Monty Python and Sherlock and Doctor Who and Downton Abbey; in some curious way, the Bletchley story shares elements with them all (eccentricity, boffins, awkward genius, plus titled ladies and a house in the country).

They wanted to hear about Alan Turing’s tea mug chained to his radiator; they wanted senior code-breaker Dilly Knox absent-mindedly filling his pipe with sandwiches, and attempting to leave rooms via broom cupboards, and writing furious letters as a boy to Sir Arthur Conan-Doyle about logical inconsistencies in Holmes. They wanted society girls pushing each other along corridors in laundry baskets and ending up in the men’s loos. They wanted code-breakers going to the pub and conversing in ancient Greek, and Bletchley locals thinking that the Park was a special government lunatic asylum.

And the enthusiasm reaches far beyond the walls of lecture theatres — Bletchley’s young maths undergraduates and brilliant female linguists and Wrens and honkingly posh debutantes have cracked American pop culture, too. While there, I was invited on to American radio for the simple reason that the ITV thriller series The Bletchley Circle, in which four former code-breaking women become detectives, has developed a devoted cult following over there. There was bafflement that the series had not been renewed. How could we British not demand more? I was also at the International Spy Museum in Washington DC: all they wanted to hear about was native British ingenuity, and the fact that 007’s creator Ian Fleming was a regular visitor to Bletchley during the war.

Now, you might think from all this that what the Americans really wanted from our story was this: bumbling intellectuals winning the day, simply by being a bit bonkers.

But the understanding goes deeper — the nerds over at Google and Apple, with their stylish San Francisco campuses, have come to revere the name and intellect of Alan Turing. He was, after all, in philosophical terms, the father of modern computing. At Bletchley, the first proto-computers were brought into being by Bill Tutte and Tommy Flowers. They too are getting the love.

What’s interesting, though, is that these modern computer folk don’t seem to be extending their veneration to similar American computer pioneers who worked on the wartime Manhattan Project. They are saying: give us the tweed and Fair Isle and received pronunciation. Google even recently bought Alan Turing’s papers and donated them to the Bletchley Park museum in Buckinghamshire.

The museum, which has seen visitor numbers rise to 190,000 this year, cheerfully acknowledges that many among those are from across the Atlantic. Quite right too, in fact, given the fact that there was a serious American code-breaking presence at Bletchley in the war. ‘The special relationship between the UK and the US probably began during the Great War with military collaboration as well as the limited sharing of intelligence,’ says the Park’s CEO Iain Standen. ‘The latter was further cemented at a historic meeting which took place at Bletchley Park on 8 February 1941. Four American cryptanalysts arrived with two replicas of Japan’s diplomatic cipher machine, which they presented to their British counterparts. The machines would enable the British to join the US in reading Japan’s diplomatic messages.’

Seventy-three years later, an ever-increasing number of Americans are making the pilgrimage to Bletchley. Not too long ago — and this is top secret, mind, so keep it under your hat — a member of the cast of The Simpsons made a quiet private visit to Bletchley Park museum and met a couple of the code-breaking veterans. It was an act of personal homage to the thousands of men and women who had worked with such intensity in those absurdly basic wooden huts. I am not at liberty to say which Simpson it was, but the visit was appreciated. One veteran told me afterwards: ‘He was charming. What is this cartoon? Would I enjoy it?’

Oh, but there is a bitter, bitter twist! Because now the Americans have cause to combust with indignation. Think of all those brilliant and distinguished US code–breakers — from Telford Taylor to William (Bill) Bundy, who adored the Park’s chaos and lack of hierarchy and insistence on regular tea-breaks — and then listen out in vain for any suggestion of an American accent in The Imitation Game. The poor Americans have been casually airbrushed out of the story. Of Uncle Sam, not a squeak. Well, as my Bletchley veteran would blithely say: ‘A little dramatic licence here and there.’