I have holidayed in various ways over the years – from backpacking and youth hostelling all the way up to a weekend in an exclusive Piccadilly hotel apartment, and from sharing a mountain spa with monkeys in Japan to navigating a narrowboat along the Shropshire Union.

One popular mode of travel that I have never sampled – or had the urge to sample – is cruising. The idea of spending my days in a floating Harrods, out of sight of land and sharing plush interiors with wealthy retirees from Florida, had never appealed. Of course, my stereotypical picture may have been skewed, but the price of cruising was always too high to tempt me to find out.

A new cruise company called easyCruise, I was informed, was very different, and since it was the latest brainchild of Stelios Haji-Ioannou – the man behind easyJet, which has revolutionised air travel in Europe – if any cruise was worth investigating, then this must be it. Could Stelios transform the concept of cruising as he had air travel? The maiden voyage of easyCruise Life – a one-week cruise taking in Kalymnos, Kos, Paros, Mykonos and Styros, as well as Bodran in Turkey – seemed the perfect way to find out.

The first element in the revolution – as with easyJet – is the price. A berth on the one-week cruise of the Greek Islands starts at little over £100. That’s not £100 a night, which would still be a fraction of a normal cruise ship’s rates, but £100 for the seven-day cruise!

Unless money (or the lack of it) is of no interest to you, that should have grabbled your attention from the start. But if a rock-bottom price were the only innovation, then you would still be faced with the format of the cruise itself. A floating Butlins is hardly more appealing – to me, at least – than the Harrods variety.

This reservation is blown away by the second step in Stelios’s plan: the scheduling of the sailing times. The ship sets sail at 6 or 7am each morning, arriving at its new destination at 10 or 11am. It doesn’t sound like much of a revolution, I know, but see how it transforms the day:

You wake up at a good holiday hour, have a quick shower and then head to the restaurant for breakfast (optional extra). Just as you are draining the last of your coffee (another option), look out across the shining blue sea to discover the day’s destination hove into view (complimentary).

Once you dock, you are free to leave the boat and have the whole day to explore... and the night too, if you so desire. You are asked to be back on board 30 minutes before sailing, so most days that means at 5.30 or 6.30am.

You can party all night – if you are of the age to party. Or if you prefer to explore, you can rent a car for the day, even spend the night elsewhere on the island as long (as you remember to set your alarm). Or you can do what I did most days: a bit of sightseeing, a bit of sunbathing, a bit of eating, and a little bit of drinking. Then it’s back to your cabin for a bit of shut-eye. And after breakfast the next day, you’re off again in a new place.

The third part of the revolution is, to quote Stelios, who accompanied us on easyCruise Life’s maiden voyage:, “Everything is a la carte.” Stelios is a businessman – a very successful one – and there is no way to turn a profit by charging people pocket money for the holiday of a lifetime. So the swimming pool on the ship is free, as is the deck you promenade on and the air you breath while you do it, but just about everything else comes with a price.

You pay for your coffee, your meals (want butter with your toast? it’s an extra 30¢.), gym equipment, island tours, spa treatments, and so on, and you pay just as much for them as you would elsewhere. But the beauty of it is that if you don’t want them, you don’t have to have them. So if you’re on a strict budget, you could wait till you are ashore to eat, drink and amuse yourself. (You are asked not to bring food and drink on to the ship.)

If you have the funds, and wish to travel in style, you can upgrade to a plusher cabin and avail yourself of many of the luxuries you would expect on a cruise ship.

The ship set sail from Piraeus at 6pm on the Saturday, and since it was the maiden voyage, Stelios bought a round for everyone in the bar and restaurant, and also hosted a buffet for all the guests.

When asked about his plans for this new venture, Stelios stressed his hope that the prices would also attract Greek tourists to their own islands. It may well happen, but on the maiden voyage the only Greek was Gerry, a gay Greek ex-housemate from Big Brother, travelling with his press agent and two young journalists from Love It! All the same, the reasonable prices attracted a much more varied clientel than a regular cruise.