Their adventure began four years ago. John, an art director, and Jane, a make-up artist, were both self-employed and their work was reasonably flexible. They decided to buy a holiday home in Europe but had no idea about the best location. They agreed that it would be a great opportunity to take a year out to look at different countries and to allow them to spend more time with their children while they were still young. They couple bought a six-berth Winnebago motor home and set off on their travels with Daniel, 7, Matthew, 6, and twins Milly and Sarah, 4.

John says: “It seemed like the ideal way to research our project and we were all really excited. But there were times when we wondered why we had decided to live in a bus with four small children for a year.”

The couple had some reservations about living in a confined space but their initial worries soon disappeared. “The whole atmosphere changed the minute we set off — we knew we were going to have fun,” says John. “As soon as we arrived in France we spent a lot of our time outdoors — swimming, walking and just being together as a family. Most restaurants in Europe are far more tolerant of children than they are here and it was relaxing to eat out with the kids.

It was also really good for them to experience different foods, languages and cultures.”

The family spent several months travelling around France, Spain and Greece and viewed a wide range of properties, but they were struggling to find their ideal home. “We wanted a property in a lively area with good entertainment for all the family,” says John. “We did see some houses that we quite liked in the South of France, but the properties and the cost of living were expensive. Crete was interesting and we did seriously consider a couple of houses there, but after several months of travelling we realised that there was only one place that we really wanted to have a holiday home.”

The family had spent holidays on the island of Mykonos in Greece for years and had always had a fabulous time there. “I suppose we were hoping to find somewhere less expensive in Europe that had the same cosmopolitan atmosphere, great entertainment and tolerant atmosphere as Mykonos,” says John. “In Mykonos you can escape the rat race with total tranquillity or go crazy with the incredible nightlife. It seems that there are not many places where you can achieve all that.”

Mykonos has been the haunt of celebrities ever since Jackie Kennedy and Aristotle Onassis began courting there. Forty years on, the island is still beautiful, highly desirable, and definitely the place to party.

Once known as the gay capital of Greece, Mykonos is one of the trendiest destinations in Europe, and it is easy to see why it became so popular. The picture-postcard town has whitewashed houses, sandy beaches, a beautiful harbour and hundreds of pink and blue domed chapels scattered across the hillside. In the Sixties, it became the holiday destination for the rich and famous and it still retains its reputation for decadent living.

The main town is crammed with designer shops and stylish restaurants and it has a wild club scene. Extravagance is the norm on Mykonos — some hotel guests sunbathe around a pool on four-poster beds with silk sheets and scatter cushions. Wealthy Athenians pop over to Mykonos to party at weekends, the clubs vie to be the most outrageous and everyone is happy to flaunt what they’ve got.

John says: “We gave up our search in Europe and stayed on Mykonos for four months. We had a brilliant time, but it was impossible to find anything to buy. We thought we might be able to buy some land, but everything was really expensive and was snapped up very quickly.”

It was only after they returned home to the UK that a friend contacted them to tell them about a detached villa that was for sale. The property had four bedrooms, an enormous terrace and a plunge pool. It was for sale for €350,000 Euros (£280,000).

“It was way over our budget,” says John, “but we rushed out to see it anyway and absolutely fell in love with the place. It had the most amazing views over the harbour and was only 350 yards from the beach. We decided that we would have to go for it and, after a rather drunken evening with the owners, we offered the full asking price.”

The transaction went through smoothly and for the past four years the Grisham family have been holidaying in their hillside home about 3km from Mykonos town. Their days are spent swimming and fishing and in the evening they go to restaurants or bars in town, where they can marvel at the glitzy, decadent nightlife.

The Grishams appear to have made a shrewd investment. During the past four years, Mykonos has become even more fashionable and property prices have escalated sharply. John and Jane were both amazed when their villa was recently valued at €645,000. Yvonnie Debia, director of Ace Real Estates in Mykonos, was not surprised. She has seen the demand for homes on the island increasing and is convinced that prices will continue to rise. She says: “Mykonos has always been popular and expensive, but nowadays it is known as a high-society island and it attracts a wealthy crowd from all around the world. There is still a large gay community, but this no longer the dominant feature of the island. In the past five years many more luxurious hotels have opened here and they are attracting even more affluent visitors. I do have a small studio for sale at €150,000, but a luxury villa with sea views will sell for millions.”

The Grishams are delighted with their house on Mykonos. “We had a great year travelling around to find our new home,” says John. “It seems that we made a really good investment and, most importantly, we have had the best time with our children. Travelling from place to place in our Winnebago was a far more satisfying experience than sitting at home researching the overseas property market on the internet. We did spend a year finding our holiday home, but now we are certain that we have found the perfect place for us.”

Ace Real Estate and Rentals: telephone 00 30 6947684589

More Greek properties for sale from A Property in Greece, telephone 020 8467 5246.

Times recommends

• Second homes: credit crunch casualty or money-spinner?
• How I built my own sliding house
• Top 10 incentives for house buyers