The words on the destination board at Liverpool Street station - “14.25 Boat Train: Harwich International, Hamburg” - were the trigger. Not any old train. A boat train: comfortable seats, big windows, no stops. The holiday had started.

Why did this matter? One part nostalgia, and three delusion, I suppose. But then, to be able to give yourself delusions of grandeur on an under-Pounds 100 holiday can’t be bad.

I was on my way to Hamburg, driven by vicarious nostalgia for five teenagers who went there 38 years before me. And especially the fifth one, Stuart Sutcliffe, the one who stayed behind. I wanted to see if there was anything left of the Hamburg that played such an intriguing role in the evolution of The Beatles.

They first went to Germany in 1960 by boat, so I would go by boat. In 1998, only one company - Scandinavian Seaways - offers regular sailings to Hamburg. Off-season, it advertises short “cruisebreaks” to Hamburg from as little as Pounds 59, depending on the date of travel and numbers sharing cabins. Not bad for a 700-mile round journey, two nights’ bed and breakfast, and a visit to a great city. What could be the catch?

The MS Prince of Scandinavia was a reassuringly large, white vessel, towering over the terminal buildings at Harwich. The ship was a blend of ocean-going liner and car ferry - and, given the number of English and German school parties that take advantage of low group rates, a floating school as well.

The cabin was spartan in a pleasingly nautical style - bunk beds, small bathroom with shower, and a porthole (which made up for a lot). Only as I flopped on the lower bunk, waiting for the ship to sail, did I realise just how much time I would be spending on board. Twenty hours there, and 20 back. Subtract 16 hours for sleeping, that leaves 24 hours for enjoying the facilities - bars, restaurants, nightclubs, sauna, shops, a cinema. I started to understand the economic logic of the minicruise.

A few hours later, I watched the evening sun catch the dome of Sizewell B nuclear power station on the Suffolk coast - a new take on the last of England. I had a smorgasbord meal - and drifted towards the bars.

Then something odd happened. My impatience to arrive slipped away. I had adjusted to the rhythm of the cruise. I drifted into a beer-fuelled exchange with three youths pursuing their own version of Hamburg as the “cradle of British pop”. Or was it Hamburg, the capital of sin? Probably both.

Next morning, mist over swirling brown water, a distant shoreline with neat, toy-like houses. This was the Elbe estuary. We were already in Germany, but Hamburg was still 70 miles upriver. You know you’re nearly there when you hear the tinny strains of a national anthem (in this case, Denmark’s) blaring from bankside loudspeakers - every foreign ship is welcomed this way.

At midday, there was Hamburg in all its glory and grimness. On one side, tall, patrician villas and parkland, bulbous Baroque church towers, green gothic spires. On the other, docks, the great Blohm und Voss shipyard - more docks.

Deposited at the western fringe of the city, I set off through an area of semi-derelict dockyard buildings, then into Fischmarkt, where yuppification is well advanced. On Sundays this becomes a heaving street-market selling almost anything - including fish. But that day it was empty, except for some computer types in search of a trade fair. I walked briskly past a newly-opened Conran shop.

I decided to stroll into the centre before getting down to the serious business of rock and roll. A mistake - Hamburg has as much of everything as any other metropolis - including traffic, pollution, drab streets and insects that bite.

It also has an extraordinary number of museums, churches, parks and waterways, as well as the great central attraction of the Alster lakes, around which leisured society revolves. A coffee bar on the “little” Alster gave me the strength to continue, via an arcade of stunningly expensive shops, into the Rathausmarkt, or town hall square. The square is lovely - the Rathaus a monster of mid 19th-century eclecticism - with six more rooms, I’m told, than Buckingham palace.

A plaque on the great St Petri church reminds visitors that in 1944 much of Hamburg was devastated by British bombs. The street-plan of the old centre remains, but most of the buildings and their occupants were vaporised. This was a cue for me to sink into the earth, and to brave Hamburg’s rapid-transit rail network.

It took five minutes to work out how to buy a ticket, destination Reeperbahn - the epicentre of everything that gives Hamburg a bad reputation. I emerged into a wide street of ugly, low-rise buildings festooned with neon and Day-Glo invitations to watch live sex shows.

Here in this mess were the clubs - the Indra, the Kaiserkeller, the Top Ten - where The Beatles, and many other aspiring bands, had been made or broken.

Somewhere nearby was the bar where doomed bassist Sutcliffe befriended photographer Astrid Kircherr and her existentialist student friends.

I set off through the back streets of St Pauli, famed as the reddest red-light district in Europe. The music clubs looked more beguiling here, away from the sex-tourist main drag. Total dives, plastered with the usual mix of fly-posters, anarcho-punk slogans and NYC-style graffiti. Here - I imagined - were places where a latter-day Lennon might feel at home.

Deeper research was necessary - but I had less than an hour left. A dash through streets of crumbling, squatted tenement buildings, through squares with sound systems just cranking up, down flights of steps towards the river. Huge groups of German teenagers were being herded on board.

Back on deck, my mission largely unaccomplished, I reflected that this weird little holiday was not over yet.

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