When the Nazis came to power in Germany in January 1933, Fritz Lustig, my father, was a 13-year-old schoolboy growing up in Berlin. He was a budding musician with dreams of becoming a professional cellist but, by the time he left school four years later, it was clear that under the Nazis, even though his family had largely cast aside their Jewish heritage, his options were going to be extremely limited.

Neither he, nor any of his anxious relatives, could possibly imagine the scale of the horrors that lay in store – but after the anti-Jewish pogrom of Kristallnacht in 1938, it was impossible to ignore the gathering storm clouds.

So, like millions of young men before him and since, he decided that his future lay away from home, and in April 1939, two weeks after his 20th birthday, he became a refugee, arriving by boat in Southampton, his beloved cello clutched firmly at his side. An unaccompanied male of fighting age, seeking asylum and hoping for a chance of a better life. Sound familiar?

Admittedly, he didn’t clamber ashore after having risked his life crossing the Channel in an inflatable rubber dinghy. But he was a foreigner, with a foreign accent and no qualifications other than his school leaving certificate. He was the sort of undesirable alien referred to by a London magistrate, and quoted approvingly in the Daily Mail, in 1938: “The way stateless Jews and Germans are pouring in from every port of this country is becoming an outrage …”

Then, as now, the outrage was unwarranted. In the years leading up to the second world war, between 70,000 and 80,000 Jewish refugees were allowed into the UK. But up to 10 times as many were refused entry. Among them was my maternal grandmother, who was shot by a Nazi execution squad in 1941.

While researching my family history, I have frequently been struck by the parallels between the experiences of the 1930s refugees from Germany and Austria and those arriving on our shores today. Whereas in the 30s, Jewish refugees were often demonised as work-shy Bolsheviks or worse, today’s refugees from countries such as Sudan, Eritrea, Afghanistan and Iran are portrayed as potential Islamist terrorists. There is nothing new about fear of the foreigner.

In July 1940, the police came looking for my father, as he knew they would, even though he was in Britain perfectly legally. The Nazis had swept through Europe and were threatening a cross-Channel invasion from northern France. Churchill feared that there might be secret Nazi sympathisers among the UK’s refugees and issued his notorious order to “collar the lot”. My father was arrested and shipped off to the Isle of Man, where he was held as an “enemy alien” in an internment camp behind barbed wire.

The camp was, in reality, a parade of sea-front hotels and guesthouses, remarkably like the hotels used to accommodate asylum-seekers today – and the first thing my father did when he got there was volunteer to join the British army. It took just six weeks for his application to be approved, and while he was waiting, he and other detained refugee musicians entertained their fellow prisoners with a series of impromptu concerts.

So here’s a “what if?” question. Suppose some of today’s unaccompanied, male refugees of fighting age were offered the opportunity to join the UK’s armed forces instead of languishing in hotels or on unused military bases. Would some of them be tempted? Even if the UK, fortunately, is not facing the threat of invasion from a fascist army on the European mainland, might this be a way to fill some of the forces’ recruitment shortfall?

And if that is a step too far, how about recruiting asylum seekers to become builders’ apprentices, just as my father was back in 1939 as a condition of his visa? (Somewhere on the A1307, just outside Cambridge, there still stands a house that he helped to build.)

It is no secret, after all, that the British construction industry is desperately short of labour, and the government is already planning to invest £600m to train up to 60,000 engineers, bricklayers, electricians and carpenters. Why not use some of the money to train asylum seekers?

My father’s career as a builder was short-lived. Once war was declared, housebuilding came to a standstill, and he ended up working first as a cleaner in various Cambridge colleges, and then as a gardener at a school in the East Midlands, which is where the police found him.

Once he had been released from internment and had enrolled in the British army, where he spent three years playing his cello in an army orchestra – not his idea of how he could best contribute to the defeat of the Nazis – my father was recruited into a top-secret military intelligence unit, eavesdropping on the bugged conversations of German prisoners of war and picking up invaluable nuggets of intelligence. It was quite a leap from when he had been classified as an enemy alien and labelled a potential threat to the UK’s national security.

It was also, according to the second world war historian Helen Fry, who has written extensively about the unit, “the biggest bugging operation ever mounted against the enemy in British history.”

The unit’s commanding officer, Lt Col Thomas Kendrick, a long-serving MI6 spymaster, told my father that the work he was doing as a “secret listener”, spending endless hours with headphones clamped to his ears, listening out for the prisoners’ indiscretions (“The interrogator wanted to know all about our secret missile development programme at Peenemünde, but of course I didn’t tell them a thing …”) would be a lot more important than if he was firing a gun or fighting on the frontline.

Which turned out not to be an exaggeration, as it was careless prison cell talk about the “secret weapons” being developed at Peenemünde that enabled the RAF to unleash Operation Hydra against the Nazis’ V1 flying bombs – known as doodlebugs – in August 1943.

As soon as the war was over, my father became a British citizen. By definition, therefore, and in law, he was now British. But was he? Really? With a German name and a German accent?

Not according to today’s ethno-nationalists, who argue that in order to qualify as a real Briton, you must be able to trace your good yeoman ancestry back for several generations. According to Charlie Downes, spokeperson of Restore Britain, a far-right party that is backed by Elon Musk and makes Nigel Farage’s Reform UK look like a bunch of wishy-washy liberals: “Britain is a people defined by indigenous British ancestry and Christian faith.”

Which rules out, just to take a few random examples, Zia Yusuf of Reform UK, whose parents were immigrants from Sri Lanka; Rishi Sunak, whose Indian-origin parents were immigrants from east Africa; Kemi Badenoch, whose parents came to the UK from Nigeria; and deputy prime minister David Lammy, whose parents were from Guyana.

It would also rule me out, born and brought up in Britain, with two immigrant parents, and speaking with an impeccable BBC accent.

Were my parents somehow less British, however valuable their wartime work might have been (my mother, Susan, another refugee, also worked for MI19, the “secret listener” unit, which is where she met my father), just because they celebrated Christmas, as Europeans, on Christmas Eve rather than Christmas Day?

Where do you draw the line between honouring your family’s cultural and religious traditions and adopting the traditions of your new home country? Are my British-born Greek Cypriot friends somehow less British because their children learned Greek? Are British Muslims less British because they mark Ramadan?

My father’s family had a long history of assimilation. His own parents were married in a non-religious wedding in 1903, and he and his three siblings had all been confirmed into the Lutheran church. No surprise, then, that when my brother and I appeared on the scene in the years after after the second world war, neither of us was taught to speak German. What mattered most to our parents was that we should fit in, indistinguishable from our “ethnically British” friends.

My father wrote in his privately published memoir: “However much I have tried to acclimatise and integrate during the 77 years I have been in the UK, I will always be somebody of central European origin, quite apart from my accent. Unless you were born and grew up in this country, you will never be an Englishman, and nobody will call you that. But all the same, I call Britain my ‘home country’, as I feel at home here, and I am glad this is where I lived my life.”

So determined was he to “acclimatise and integrate” that he tried for a time to change his given name at his place of work from Fritz to Frank, painfully aware that for many Britons, Fritz was the generic, derogatory name they gave to their wartime enemy. I still have vivid memories of my 1950s schoolmates zooming around the school playground, arms outstretched as they pretended to be heroic RAF Battle of Britain pilots and shouting: “Take that, Fritz, you filthy Hun …”

My father’s attempted name change didn’t last long – all his musician friends had always known him as Fritz and it got too confusing when his work world and his music world collided – and he was never tempted to go the whole hog and change his family name as well. (One Australian branch of the family did become Lusty, which he regarded as even worse than the original. I will always be grateful to him for his good sense.)

For much of his adult life, my father could have been best described as self-effacing, and happy to stay in the shadows (except when playing his cello) and let his far more outgoing wife do the talking. But, when I got married in 1980, he made a witty, well-received speech to our guests and finally decided that his, by now, slight German accent was no longer an impediment to revealing more of himself.

And, when the details of his secret wartime work were revealed 20 years later, there was no stopping him. As one of the last surviving secret listeners, he was constantly being interviewed on radio and television. “You know me,” he said, when I queried whether he was perhaps doing too much. “I’ll talk to anyone.”

His last TV interview was broadcast the day after he died in 2017 at the age of 98. His death was reported by the BBC and marked by obituaries in the Guardian and the Times. Not quite up there, perhaps, with fellow refugees such as Albert Einstein, the Google co-founder Sergey Brin, Freddie Mercury, Marc Chagall or Madeleine Albright – but one more refugee, nonetheless, who made a lasting contribution to the countries that granted them sanctuary.

And the Cello Came Too: A Story of Survival by Robin Lustig is published by Marble Hill Publishers (£20)