Balearic bliss: Majorca is the perfect destination for a civilised family holiday

The water's lovely: To the north of the island, safely away from party hell, lie sheltered beaches such as child-friendly Formentor (Alamy)

Last summer's most fashionable Balearic backdrop? Not overhyped Ibiza, nor even its louche neighbour Formentera. No, in August, according to the pages of Grazia, there was only one place to be. After all, why else had Britain's top paparazzi magnets decamped en masse to our tiny stretch of Majorca's spectacular northern coastline, the one to which we'd reluctantly waved goodbye only days before?

There were the Camerons in matching dark-blue in Pollença's pretty town square. There was Tour de France winner Bradley Wiggins letting down those famous sideburns (and sneaking a cheeky post-Olympics fag) on the local harbourside. And there was Kate Moss (plus entourage, of course) relaxing a short hop away in hippie-chic Deia.

That the country's Prime Minister, national sporting hero and pre-eminent supermodel should be soaking up the sun on adjacent loungers may have come as a shock to those whose image of this island is based on sangria-soaked repeats of ITV's Magaluf Weekender. But our celebs are parents all – and to those who treasure Majorca's quieter north-eastern corner as the perfect destination for a civilised family holiday, it was really no surprise at all.

As more people are coming to realise, there are two sides to this island – safely separated by the jagged peaks of the Serra de Tramuntana, which divide the island from east to west. And over here to the north, the fleshpots of Magaluf and Palma Nova seem a world away, as the hillside tumbles down through groves of orange, lemon, olive and almond trees, past some of Europe's most expensively renovated farmhouses, before plunging over granite cliffs to secret coves, such as remote Cala Tuent, and more sheltered, child-friendly beaches, such as Formentor, lapped by a crystalline sea.

Lacking an invite from the Wigginses, the Mosses or the Camerons, we stayed at the spacious Villa Pepi, outside the elegant little town of Pollença, famed for its cobbled streets, perfectly preserved buildings – admired by Churchill as well as the current PM – and the 365 steps that lead to the hilltop known as Calvari, scene of dramatic torchlit parades.

With its luxuriant garden, mountain views, fabulous pool and satellite TV, it proved the ideal base – and at first we found it hard to drag ourselves away. Before long, however, we ventured out – picking up supplies at the busy market, bagging bargains at the Camper shoes factory shop, lingering over delicious tapas (try 13% in Calle San Feliu) amid the unmissable medieval magnificence of Palma's Old Town, and returning again and again to the light- demerara sands of Formentor, fast becoming our children's favourite beach in the whole wide world.

One memorable day, we drove high into the hills, visiting the cool cloisters of the ancient monastery at Lluc, home to Spain's most famous boys' choir, then zig-zagging down through hairpin bends and past mountain lakes, pausing to admire the vertigo-inducing views at the Mirador de Ses Barques, before descending again to the bustling quayside at Port de Soller and one of the freshest plates of prawns we'd ever tasted.

From Soller, we drove on a while to a fêted country-house hotel, the Gran Hotel Son Net in the village of Puigpunyent. Only a 20-minute drive from the bright lights of Palma, this beautifully converted 17th-century finca, perched on a hillside above a verdant hidden valley, seems to belong to a more rarefied world, with private cabanas around the pool, paintings by Hockney and Chagall on the walls, and what may be the most romantic restaurant terrace in the Med.

This is the high life, we thought, settling in to watch the stars come out with a cool white from the estate's own vineyard. As we perused the dinner menu, our waiter told us that the hotel's regular guests include another Tour de France winner, the Spanish champion Alberto Contador, who bases himself here during training. For perhaps the first time in our lives, we wondered whether all these cyclists know something we don't.

Mallorca Farmhouses, the award-winning accommodation specialist celebrating its 25th year, offers a selection of self-catering country cottages, converted farmhouses and luxury villas; prices for Villa Pepi from £846 per week (0845 800 8080, mallorca.co.uk). Rooms at Gran Hotel Son Net from €155 per night (sonnet.es)

More family frolics

1. Take a bite-sized cookery course led by River Cottage chefs, at Hugh’s home in Devon. Try out one-day sessions geared to families, such as Pizza Bites (rivercottage.net)

2. Learn how to track animals as a volunteer in the Kenyan wildlife conservation area of Rukinga Sanctuary (campsinternational.com)

3. The newest craze to hit the waters of St Lucia, snuba-diving combines scuba and snorkelling, a stress-free way to get little ones below the water. Try it at the revamped Sugar Beach resort, in the Pitons National Park (viceroyhotelsandresorts.com)

4. The Brothers Grimm penned their first fantastical tale 200 years ago this year. Explore the 370-mile Fairy Tale Road, from their birthplace in Hanau to Bremen, the landscape that inspired Rapunzel, the Pied Piper and more (germany.travel)

5. Go camping with a concierge. Head to Cornwall and get everything from your tent to your food delivered, set up and all your family’s activities arranged (adventuretemples.com)

6. Encourage your teens to roll their eyes to the heavens, on a new family astronomy and adventure holiday to the Sinai Desert (adventurecompany.co.uk)

7. Stay 30ft up a redwood fir on a château estate deep in the Normandy woods, in a treehouse designed to resemble a medieval castle. (chateaudelagrandenoe.com/grande-noe)