I had to look twice. Why was that imposing block of black-and-white flats sitting slap-bang in the middle of Dover Harbour? The port has long been home to Saga's cruise armada and big ferry companies such as P&O, but this was something else.

Look again, and you realised you were gawping at the mighty Eurodam, the gleaming new 86,700-tonne pride of Holland America Line's 15-ship fleet.

Surprisingly, a four-day mini-cruise at the start of the summer, around the Channel with whistlestop visits to Zeebrugge, Cherbourg and Guernsey, might have cost you only £380.

Mini-cruises sailing from British shores have been a big seller this summer – and I can see why.

Passengers get the flavour of a new ship, to see how it compares with their usual cruise holiday.

Mini-cruises are also easier for agents to sell, because they're cheaper.

But the Eurodam sitting proudly in Dover Harbour stands for something else, too: cruise lines such as P&O, Fred Olsen and Saga, which have had a monopoly on sailings out of Britain for years, face an invasion from European and US rivals.

Celebrity, the upmarket wing of Royal Caribbean, also starts Southampton sailings next summer.

So what can the Americans bring to the party? For starters, they call their cabins staterooms, which puts you in a more glamorous frame of mind from the start. Ours put plenty of space into the double bed, rather than the sitting area, and included a bath. The cushions on the balcony seats were lifted inside by the steward each night.

However, the narrow wardrobe might irritate on a longer voyage.

As a brand, Holland America harks proudly back to glory days of classy Transatlantic travel in the mid-20th century, with pictures of its former ships lining every corridor.

The Lido restaurant, Eurodam's casual place to eat on most days until midnight, has a fantastic selection of food to suit most diets.

In the evening, you can eat at fixed or variable times in the main Rembrandt restaurant, or make a reservation in four other speciality eateries, where the premium to eat ranges from nothing to $20 (£12) per head.

The choice includes the Canaletto (Italian), the Tamarind (Pan-Asian) after a drink in the exquisite Silk Den nearby, and the Pinnacle Grill – with massive steaks that could have been smuggled from the pampas of Argentina. The last two are cosy, intimate places, with service standards impressive for a big superliner.

The Eurodam also has cabanas: tented cabins crammed with chaises, ottomans and settees, and stocked with bathrobes and plush towels. The occupants sit back like Roman emperors, to be fed chocolate-covered strawberries and Champagne by obedient flunkies.

On port days, cabanas rent from $45 (£27), on sea days from $50 (£30).

I settled for a more spartan routine, setting my alarm at 6.45am.

You can have the pool on deck nine – enclosed by a Wimbledon-style sun roof – all to yourself for 20 lengths, surrounded by gently erupting fountains.

Or you can head for the gym, where the "stretch and breathe'' routine supervised by a muscle-bound gentleman from Eastern Europe touched parts I never knew I had.

Out of 2,108 passengers on board, just six showed each morning for Vassily's daunting half-hour routines.

Our afternoon tour of the Cherbourg Peninsula cost $88 (£53). Add another 5.50 euros (£4.75) to get into the museum at Sainte-Mere-Eglise, the first town retaken by US troops in Western Europe.

For other stops, it was easy to go our own way, exploring the narrow medieval streets and splendours of ancient Bruges and then more recent antiquities in friendly St Peter's Port, on Guernsey.

Back on board, there was no shortage of things to do.

Where Eurodam really sets a marker for its rivals is a revamped information area including the library – a rather quiet, stuffy room on many ships – which blends into an open-plan knowledge section.

Explorations Cafe, alongside the Crow's Nest on Deck 11, has CD and videos for hire and an Internet library.

There is no particular "wow" factor about the central atrium, but Holland America's other standout feature is a Culinary Arts Centre, a £1m demonstration kitchen display area where a snappy film introduces chefs and other experts to dissect the finer points of food.

It sounds sexy, but talking about food while you cook is not as easy as celebrity chefs make it look.

The talk which most galvanised my fellow passengers – well, 50-plus ladies anyway – came from eternal "Green Goddess" Diana Moran.

The last stop, as we hurried back to Dover, was the Greenhouse Spa. My $75 (£45) session in Men's Grooming promised many delights, and I can recall a head massage of sorts as I gently nodded off with views across open seas.

But when I felt my chin, I realised the treatment had also included the smoothest shave I'd ever had, expertly delivered by Ray, a demon barber from the Philippines who'd spent much of his life with Holland America. He looked much healthier than me, which might be a suitable tribute to the line's bracing lifestyle.

Info

Best for: Holland America's Eurodam is ideal for upmarket cruising for couples, rather than families.

Time to go: To the Caribbean in winter, back in Dover next spring.

Don't miss: Speciality dining.

Need to know: Get it right with smart casual.

Travel Facts: Jeremy Gates was a guest of Holland America, which offers ex-Dover cruises on Eurodam from £949 for eight nights in May/June 2010, with Baltic voyages from £1,329.

HAL reservations: 0845 351 0557, or:

www.hollandamerica.co.uk