‘What was it like growing up in Liverpool?’ a journalist asked John Lennon. ‘I didn’t grow up in Liverpool,’ he replied. ‘I grew up in Hamburg.’ My father grew up in Hamburg too, at the end of the second world war. The city had been bombed to smithereens. Cigarettes were the only currency, and my grandma had to trade her jewellery for food. When she met a British soldier who offered to take her to England, she grabbed this lifeline with both hands. If only she were alive to see her smart home town today.

When the Beatles came here in 1960, they stayed in St Pauli, the dockside red-light zone. When I first came here in 1990, St Pauli was still sleazy. Now it’s the height of chic. Some of the old strip-clubs have survived, but they’re outnumbered by swish coffee shops. Sight-seers forage for Beatles souvenirs amid the sex shops of the Reeperbahn. Through a friend, I met an old man who’d been a bouncer at some early Beatles gigs. He said Lennon was a loudmouth, Ringo Starr was easygoing and George Harrison never said a word. He liked Paul McCartney best.

You can see why Liverpool lads would have felt at home here. A Hanseatic port, Hamburg has always been cosmopolitan, Germany’s gateway to the world. The huge container ships in the harbour are a looming, thrilling presence. I like to walk along the waterfront, from Landungsbrücke to the Fischmarkt, and stop off at the quayside stalls for cold beer and pickled herring. Hamburg’s hearty street food reflects its rugged heritage; this is a city built on trade.

Hamburg’s centrepiece is the Alster, a large lake crisscrossed by ferries, right in the heart of town. The cries of greedy seagulls carry across the water, and the horizon is flecked with the sails of distant yachts. My grandma had a painting of this scene, one of the few mementos she brought to England. Some winters this lake freezes over: when he was a child, my dad walked across it.

My grandma’s old house is on a hill above the Alster. The house next door belonged to a nice Jewish doctor who disappeared. He nursed my aunt when she was small. Then one day an ambulance arrived and took him away. His house was handed over to the chief of police. After the war the police chief vanished too, and it was requisitioned by British soldiers. My grandma fell for one of them. By the time my grandfather returned home from the Wehrmacht, she’d already made up her mind.

My grandparents had first met at the Vier Jahreszeiten, Hamburg’s grandest hotel. It’s palatial, with a wonderful old ballroom, but I prefer the Atlantic, on the other side of the Alster. Built for first-class passengers en route to America, it still feels like an ocean liner. The surrounding area, St Georg, is a bizarre blend of style and squalor: its leafy avenues boast some of Hamburg’s best bars and cafés, while its station is a rendezvous for every sort of down-and-out. A lifetime since my grandma left to try her luck in England, her forsaken heimat has more millionaires than any city in Europe. But, as John Lennon understood, it wouldn’t be the same without a bit of rough.