Mallorca long ago shrugged off its 1970s sangria hangover, only to spend the following decades eclipsed by its naughty little sister, Ibiza. And a good thing too, its growing band of devotees would say. Gradually its understated charms, especially in the unspoilt north, have made it the destination du jour among those who might once have sniffed at the idea, as if at a corked rioja. No surprise, then, that eventually Dave and Sam would fetch up at a Mallorcan pavement cafe for their annual Boden holiday photoshoot.

But don't let that put you off. Not only does the coolest man on earth right now, Mr Bradley Wiggins, spend large parts of the year training there, but it's also home to lovely Rafa Nadal. And according to robust journalistic sources (Guardian Passnotes no 3,230), a whole bunch of celebs have chosen the island for romantic getaways, including "Beyoncé and Jay-Z, Jude and Sienna" (do keep up, Passnotes!). Moss and co are always popping over on their yachts from Ibiza, apparently.

I can report that we didn't spot a single pop star or Prime Minister during our week in Mallorca, but, by complete accident, we did watch the final stage of the Tour de France in the bar in Port de Pollença, where Wiggins comes with his family. Or at least that's what the barman said, and he seemed to know an awful lot about Wiggins's weight and stuff.

No sooner had Mark Cavendish crossed the finish line than my boyfriend – scarily suggestible – was round the corner eyeing up a slender little carbon number in the cycle hire shop. I fully expected him to return home sporting sideburns. But he wasn't the only one: a long line of hommes d'un certain age, of various shapes, sizes and suitability for balancing on a thin aluminium pole (members of Team GB were easy to identify, for all the wrong reasons) trailed out of the door.

The combination of vertiginous peaks, endless twisting roads and scorching heat make this the place to go for a holiday spin, it would seem. In fact, never mind A-listers, the island is suffering an infestation of Mamils (middle-aged-men-in-Lycra): everywhere you go – mountaintops, roadsides, courtyard cafes – you find fluorescent, pink-faced rashes of them.

For a crazy moment (the boredom of the queue) I contemplated hiring a bike too: but I remembered a cycling tour of Cornwall that left me with leggings dyed onto my legs for weeks afterwards, it was so wet; not that rain would be the problem here, of course.

So from early morning, I had our little villa, Casellas de Baix, amid the fields of the Campanet valley, all to myself: it's surrounded by mountains, the only sounds the gentle clink-clink of goat bells and the dreamy hum of the cicadas. Lucky Mrs Wiggins, I reflected more than once, as I lay by the pool. Pretty decor, well-tended terrace and garden – there's not much to say about the villa except that it was completely lovely.

Horse riding and kayaking are available for the more energetic, but having already shunned the cycling, I was determind that nothing was going to get me off my sun lounger. Lucky, then, that one enterprising company has set up the imaginatively titled Pampering by the Pool: there's nothing like being buffed and manicured on your own poolside to make you feel like you might just pop up in next week's Grazia. It does also make you feel a little bit silly, truth be told. But I got over it.

When the Wiggins wannabe finally hung up his cycling shorts, we were free to explore – by which I mean visit the best beaches. One day we made a pilgrimage to one of Mallorca's hidden beaches, Cala Tuent. It took about an hour and a half to drive there – but half the time if the road could be ironed flat. I'm sure there must be some other reason (the island's only power plant, say) why a country would build a road as steep and long and winding as this, but it seems that it was just to get to a very secluded, very beautiful beach. Bravo, Mallorca!

Closer to home, much less hidden but almost as idyllic, is Platja de Formentor, a strip of white sand so long that you can be sure of finding a discreet spot, despite its crowds.

The sleepy nearby village of Campanet is perfect for a morning coffee in the square – watching the locals chat and smoke, and the Mamils glug fizzy drinks and catch their breath – or an early-evening beer. The villa kitchen is tiny, but who wants to cook inside when there's a big barbecue outside, and a view to soak up with your glass of wine? The welcome book has some excellent Spanish recipes. A trip to the supermarket is never a chore on holiday: not only is everyone more tanned and beautiful than in your local Tesco, but there's live lobster at the fish counter.

One evening we ventured out to Fornalutx, "often voted Mallorca's loveliest town – if not all of Spain's", according to our guidebook. And indeed it is very lovely, a tiny medieval village sheltering beneath Mallorca's highest mountain. We managed to get an outdoor table at Ca N'Antuna (Carrer de Arbona Colom, +34 971 633068), which boasted hearty mountain specialities such as rabbit and suckling pig.

In Pollença, only a 10-minute drive from the villa, there's a huge choice of tapas bars, traditional Spanish restaurants and posh pasta places. Pollença Old Town is a typically picturesque jumble of tall, sand-coloured stone buildings, cobbled alleyways and church courtyards, crowned by the 365 Calvari steps (one for each day of the year: just the thing after pedalling those mountains) leading up to a small chapel with stunning views.

The streets and central square were decked out in strips of floaty white tissue (I don't think it was loo roll): it felt like being in a very pretty snow globe, or on top of a giant wedding cake. In fact, it felt altogether like being at a wedding party, especially on the Friday evening, when a raucous live band played and little girls and old ladies danced in the square.

It's not hard to see why the Camerons chose Mallorca: it's the perfect family-friendly island. And in September, when kids (and politicians) go back to school, it will be even more perfect as there'll be no problem finding a patch on the popular beaches. Or, with the heat abating slightly, send your other half off on a bike and get a spot of pampering by the pool.

• Accommodation was provided by Mallorca Farmhouses (0845 800 8080, mallorca.co.uk). Casellas de Baix is available for a week from 20 October for £414, then again from March 2013, from £327. Other properties on the island are available at discounts in September and October, from £1,161 for a house sleeping five. Flights were provided by Monarch (monarch.co.uk), which flies to Palma from Birmingham, East Midlands and Leeds-Bradford from £72 return. Car hire was provided by Rhino (rhinocarhire.com), from £68 for a week