SIR Antony Beevor is a bit wary of historical parallels as a rule, but since we’re here to talk about Britain’s involvement in an ill-thought-out project from the past that ended in disaster, I can’t help myself. Does Sir Antony think the subject of his latest book, the notorious Battle of Arnhem in September 1944, could help to explain a more recent ill-thought-out project by the name of Brexit? Well, yes, says Sir Antony, he thinks it might. One of the reasons we’ve ended up here? The delusions and fantasies of the past, he says.

But first: Arnhem, otherwise known as Operation Market Garden, the plan to end the Second World War by parachuting Allied troops into occupied Holland and capturing all the key bridges leading to the Lower Rhine. The idea, dreamt up by Field Marshal Montgomery, was that the operation would be a killer blow against a weakened enemy, but famously it ended in disaster. The German forces were stronger than we thought, the Allied forces ended up cut off and isolated and, after nine days, it was over.

However - even though it ended in failure - the Battle of Arnhem has since gone on to become one of the most famous episodes of the War, thanks partly to the 1977 film A Bridge Too Far. It has also become a much-debated subject for military historians: could the British have won the battle if only they had done things differently? What if they’d parachuted in a little closer to the bridges? What if the weather had been different? For years, the what-ifs have circled.

And now it’s the turn of Britain’s best-selling historian Sir Antony Beevor to tackle the subject. Sir Antony is still best known for his 1999 book Stalingrad, which told the story of the bloody battles fought in the city in 1942 and 43, and he takes on Arnhem in the same way, digging into the archives for new stories and telling them with great humanity and sensitivity. For the first time in detail, for instance, he relates the story of the Dutch civilians and how they were made to suffer for the failure of the campaign - it is estimated that around 16,000 to 20,000 died of starvation.

However, the main focus of the book is on the nitty-gritty of the campaign, and how it was planned and executed – as for the what-ifs, Sir Antony has no time for them. “What irritated me about previous books about the subject,” he says, “is that too many of them had gone in a little bit for the idea that if only this had gone right, then everything would have been fantastic. It was a bad plan right from the beginning.”

Sir Antony also rejects an idea that Arnhem might at least have hastened the end of the War. “No,” he says, “in fact, what you could say is that it gave the Germans a sort of morale boost because, having had a string of defeats in Normandy and on the Eastern front, here suddenly was a victory.”

Another fascinating thread in the book is how the Arnhem operation was led and in particular the egotism, vanity and denial of Montgomery and General “Boy” Browning, who commanded the I Airborne Corps. Sir Antony is convinced Montgomery had high functioning Asperger’s. As for Browning, Sir Antony says the general knew the facts and should have gone to Montgomery and said ‘we’ve got to rethink the whole thing’ but he didn’t because he was so desperate to command the Airborne Corps.

There is another theme about leadership in the book that leads us directly to Brexit. At Arnhem, says Sir Antony, Montgomery refused to acknowledge that Britain was now very much the junior partner in the alliance to the Americans. Sir Antony goes on: “The idea that Britain remained a first-rate power was a fantasy which Churchill desperately tried to promote, even though he knew in his heart that it was not the case. In fact, one could argue that September 1944 was the origin of that disastrous cliché which lingers on even today about the country punching above its weight.”

I ask Sir Antony if this disastrous cliché as he calls it helps to explain Brexit. “To a certain degree, yes, I think it does,” he says, “this idea somehow that we can make it alone in the world and all the rest of it. The trouble about it, and one of the reasons I am so fundamentally opposed to Brexit, is what the consequences will be.

“Now, the British economy might do really well under Brexit – it’s perfectly possible – but within the economy you can see a far greater polarisation between rich and poor – those who are going to do well under Brexit, it’s going to be a small minority – it will be the ones where Britain has virtually been turned into an offshore island and it will be profiting from even more money laundering than we’ve seen in the past. The ones who will suffer are the ones with the sort of jobs which are diminishing already – manufacturing jobs and a whole lot of other things.”

Sir Antony also sees Brexit as part of a bigger problem. “Extremism is rising again,” he says. “It’s obviously not rising in the same way as the ideologies of the 1930s. The poverty is not as bad as it was in the 1930s but it’s relative – what we are seeing in many way is fear of the future and of loss of jobs – we are going to see a degree of globalising which will have a catastrophic effect. Then you’re in to the dehumanisation of the other, then there is a danger. History is not repeating itself but we can learn from the past about what the dangers are.”

Part of the problem, of course, is Twitter, Facebook and “fake news” which can help fuel the dehumanisation of immigrants and others and promote extremist solutions. Sir Antony is pretty much horrified by it all.

“I’m terrified because we’re in a world where the dividing line between fact and fiction is becoming so blurred, it’s hardly exists any more,” he says, “As a historian, that horrifies me and terrifies me. A fact is something you assert – it started with the scientologists and their great slogan ‘if you believe it’s true, it’s true’. This is all part of identity politics – we’re in the early stages of ‘if you believe you’re female, then you’re female’. I find that slightly frightening, that ‘you are what you want to be’. Yes, that’s great, but let’s also keep our feet on the ground with a certain element of objectivity rather than pure wishful thinking.”

No one should be surprised that Sir Antony takes this stance – he’s a historian whose reputation has been built on relentless unearthing of the facts. But perhaps the key to his success is that he also presents the facts sensitively. For a time, before he became a writer, he served in the Army with the 10th Royal Hussars, but realised while there that he had joined up for the wrong reasons. As a child, he suffered from Perthes disease, which affected his hip and left him on crutches, and he thought the Army could compensate for his frailty as a child. It couldn’t.

While a writer, Sir Antony also discovered the outer reaches of his sensitivity as he came to the end of his second book, Berlin. “I did have a bit of a nervous breakdown at the end of that book,” he says, “partly because of the pressure of work and also because when Stalingrad was coming out nobody had expected it to be a success and as a result there had been no pressure from my publishers and that, combined with the horror of the book, did for me. It was a bit too much.”

In person, Sir Antony talks about his breakdown and his struggles to be a writer with the matter-of-factness of an ex-Army man, but he is engaging and self-deprecating too. He tells me his first attempt at a novel is still in a box somewhere unpublished (“thank God”) but that he’s half-written another one. The 71-year-old also says he has at least three more history books in him, although in the meantime it’s all about Arnhem.

As he’s leaving, we get talking again about why the battle endures in the British folk memory - could it be because we love it when the odds are against us? “I’m afraid we always tend to - there’s a lot of poetry like The Charge of the Light Brigade,” he says. “What poems are there about Waterloo?”

Antony Beevor is at the Edinburgh Book Festival on August 12. Arnhem is published by Penguin at £25