A cruise ship that used to be a spy ship? David Wishart checks out the born-again Seven Seas Navigator

How could you not have a good time on a Mediterranean cruise when it turns out your vessel is an ex-Russian spy ship and the handsome chap on the bridge is called Captain Romeo? And what with there being a war on and only 170 passengers showing up out of the full house of 490 who had paid to sail from Nice to Venice, the 300-strong crew of the Seven Seas Navigator was able to provide the kind of service normally reserved for private yachts such as Aristotle Onassis's Christina O, which we passed while leaving the Athens port of Piraeus.

From my perch 11 decks high, the Christina O looked tiny, but then she is – a former Royal Canadian Navy escort vessel of a few thousand tons converted into one of the world's most glamorous ships. The Seven Seas Navigator, by comparison, is 28,550 tons and also born again, its bottom five decks being thick Russian steel.

It started life as the Cold War "research vessel" Akademik Nikolay Pilyugin. Apparently, its listening gear was so powerful, it could eavesdrop on mobile phone calls in Maidstone or Memphis. It was rebuilt two years ago at the Mariotti shipyard in Genoa, and it now has all the qualities expected on the most luxurious of modern cruise liners. There are spacious cabins with private balconies, walk-in closets and 24-hour room service. Ninety per cent of the cabins are like this, which means that many passengers get on board and disappear, not to be seen until it's time to get off.

But if the service seemed particularly swift – with waiters catching forks before they were halfway to the thick-pile carpet – it should be pointed out that Radisson Seven Seas Cruises prides itself on going over the top as a matter of course. Take the menu, for example. If tonight's offering does not take your fancy, just ask for what you want, and if the chef can lay his hands on the ingredients the odds are that it will be served up with a smile. Caviar? Not an eyebrow was raised, although it was nowhere in print, at least not until a formal night. As Mike Baker, the UK sales manager for the line, would say, the menu is merely a suggestion.

Yes, we dined well on the Seven Seas Navigator. Quality was superb and portions small, a winning combination unless you want to spend all your free time in the gym or pounding the deck. And you have to be on your guard, for just when you're full of resolve to resist ritzy desserts such as Grand Marnier soufflé, along comes rice pudding. I mean, a man has his limits.

Most of the passengers on my cruise were from the US, backed up by a healthy number of British. The Americans tended to be older, and well travelled, the kind of people who were not going to be put off by the events of 11 September. But many others had cancelled, making it possible for me to embark at Athens for a four-night mini-cruise. Security was tight getting on the ship, which I liked, but it got better at reception when I exchanged my passport and credit-card imprint for a glass of champagne.

A quick tour made the point that nothing had been overlooked, including four roomy cabins for people with disabilities that are among the best afloat. In fact, the entire ship is fully accessible by wheelchair. And as an example of what you get in a ship of this small/luxury class, the smallest cabin on this vessel is more than twice the size of the smallest cabin on the world's biggest cruise ship, the Explorer of the Seas.

Our first port of call was the cricket-playing island of Corfu. I took the free shuttle bus up to the old fort for a panoramic view of the bay and the Seven Seas Navigator, then walked back the three miles or so in the warm November sunshine.

Dubrovnik, the next day's stop, was badly damaged by Serb shelling in the recent war, but the medieval city has been restored and the walls repaired. A woman at the bureau de change told me: "It would have been worse but for the old walls. They saved us again."

I paid 15 kuna (£1.20) to climb the ramparts and wonder at the skill of the engineers. I was also amazed by the cleanliness of Dubrovnik, which was reminiscent of Singapore. The people, too, were well-dressed and elegant.

Then Venice, and the thrill of sailing up the main street just as Marco Polo would have done. We went within a stone's throw of St Mark's and veered left just before the Grand Canal. Within an hour I was off the ship and on vaporetto (water bus) route 1 on the Grand Canal bound for the vaulted wooden Accademia bridge and lunch in the colourful quarter of Dorsoduro

And what of Captain Romeo? Well, when I dined at the captain's table, he proved to be a cut above other masters I've met by offering a very good French wine. We raised our glasses to Nikolay Pilyugin. I hope he was listening in.

The facts

Getting there

David Wishart joined Radisson's Seven Seas Navigator cruise (023 8068 2280; www.rssc.com) from Athens to Venice. Radisson's new Mariner will be cruising from Rome to Lisbon on 6 June. Prices start from £2,865 per person, in a deluxe suite. Navigator is in Alaska this summer, on Radisson's first world cruise from Los Angeles. En route, there is a special offer of Fort Lauderdale to Los Angeles, departing 4 May for 14 nights, from £3,895 per person, based on two sharing, all inclusive, including return flights.