Madeira: it’s like a cosy old cardigan, isn’t it? Warm but not to be seen out in. The visitors are all 93, there’s nowhere stylish to stay or eat, and nothing to do apart from look at gardens. Dull, dull, dull.

Wrong, wrong, wrong. Because, while we weren’t looking, the Atlantic’s frumpiest island got cool. Suddenly, it has designer hotels, elegant bars and cutting-edge art and architecture.

And adrenaline. Over the past couple of years, continental thrill-seekers have realised that the sheer cliffs and clear seas make this a perfect place for paragliding, diving, extreme mountain-biking... and throwing yourself down chasms and rapids in what’s fast becoming the canyoning capital of Europe.

Now, no-frills flights mean it’s cheap enough for a short break. So here’s how to do the new Madeira in four days.

Day one: off the afternoon flight and into the hotel. Quinta da Rochinha (www.pontadosol.com) is a sexy slab of minimal modernism tucked away on its own clifftop, in the village of Ponta do Sol. The position’s fantastic: all 54 rooms have sea views, but the best are 501 to 506, with a breathtaking vista of the sheer cliffs plunging into the Atlantic. It has an infinity pool, a cool lounge and uncompromisingly conceptual art on the walls. And doubles start at £65.

Over in Funchal, you could try the Asian-influenced Zen luxury of Choupana Hills (www.choupana hills.com; doubles from £200) or the equally stylish Quinta da Casa Branca (www.quintacasabranca.pt; doubles from £133;).

For dinner, which is late round here (only tourists go out before 10pm), grab a cab into Funchal’s pretty old town and head to Riso (Rua da Santa Maria 274), a knowingly sparse, whitewalled restaurant specialising in (you guessed it) risotto. Have the grilled limpets (£5.50), then the lime, black scabbard fish and roasted banana risotto (£10.50). Sounds terrible, tastes sublime.

Day two: 10 years ago, nobody in Madeira knew what canyoning was. Now, the professionals from France, the birthplace of the sport, come here to train. It’s partly the variety – there are 42 established routes – but it’s also the beauty. Many of the rivers tumble through the Lord of the Rings landscape of the Laurissilva, the 40-million-year-old laurel forest that covers much of the north side of the island.

As a result, canyoning here means wading, scrambling, climbing and jumping down through a series of magical woodland dells. It’s as spiritually uplifting as it is physically demanding.

Not that you have to be an athlete. Physically, if you can walk briskly for an hour, you’ll be fine; mentally, you need a bit of nerve to rappel down sheer waterfalls. A four-hour session with Ventura (www.venturadomar.com) is £47.

Back to the hotel for a siesta. It’s going to be a big night. Nearly 40% of Madeirans are under 25, and they want to party. They’re good at it, so join in. Start off about 11pm at the Café do Teatro, opposite the municipal gardens. It’s outdoors, it’s loungey, it’s laid-back, and everybody who’s anybody in Madeira will drift through during the evening.

The DJ livens things up about 1am, but by that time you’ll have moved on to Chega de Saudade, up the road at Rua dos Aranchos 20 (it’s a swine to find: just go up those stairs and follow the noise). It’s the flavour of the month with the local smart set, who gather in the tiny upper rooms for the splendid caipirinhas, sound DJs and arty ambience. It closes at 2am, unless everyone’s having a good time, in which case it doesn’t. It usually doesn’t.

Then into a cab and over to Camara de Lobos, a mile or two up the coast. On Friday and Saturday nights, the streets around the town square buzz with locals chatting and drinking ponchas (honey, lemon and rum). Bar Number Two is well regarded, but the throng on the streets serves as the best guide – just go where they’re going. Everyone from fashion designers to fishermen comes here to hang out. You should too. By 3am, the clubs are opening back in Funchal. Yes, opening. Vespas and Marginal (both on Avenida Sa Carneiro) are the places to go. We’re off to bed. There’s a limit, you know. We’ve got to play tomorrow.

Day three: culture calls. Casa das Mudas art centre is a modernist melange of quirky angles teetering high over Calheta, an otherwise unremarkable seaside town. It’s sensuous black lava blocks outside, a succession of yawning white spaces inside, which house a series of high-profile exhibitions. This winter, Madeiran artists hold the fort, including the high-camp photography of DD:Arte, with their kitsch recreations of renaissance masters.

More activity? The precipitous slopes are made for paragliding: you literally jump off a cliff and float down all the way to the sea, hundreds of feet below. Beginners can jump with an instructor. Prices start at £54 with Madeira Airadventours (booking essential: 00 351-964 133 907).

Or you could dive, at any one of a dozen operations across the island – try Madeira Divepoint (291 239 579, www.madeiradive point.com); there are plenty of barracudas, groupers, rays and dolphins in the clear water. Or mountain-bike – Ventura (see above) organises trips. Even going for a drive can be an adrenaline sport around here. Take a 4WD tour with Mountain Expeditions (969 677 679): climbing a lethally steep forest track in a Land Rover, with mud flying off the spinning wheels and nothing but cliffs and laurels below, is not for the nervous. A morning’s outing is £22.

A quieter evening tonight. In just four months, Armazem do Sal (Rua da Alfandega 135), in Funchal’s old town, has won a strong local following, but tourists have yet to discover its mouthwatering meat dishes, served up in a gorgeous, beamy, 170-year-old converted salt factory. You’ll hear some authentic, high-quality fado folk music into the bargain.

Day four: you’ve been busy. It’s warm. If you’re staying at one of our recommended hotels, you’ve got a lovely pool. Use it and, while you wallow, spare a thought for everyone back home who still thinks there’s nothing to do in Madeira. They’re probably sitting in the pub right now. Serves them right.

Getting there: flight time to Madeira is 3hr 40mins from London. Airlines flying there include EasyJet (from £87; www.easyjet.com), from Gatwick, Stansted and Bristol; TAP Portugal (from £109; www.flytap.com), from Gatwick and Heathrow; and First Choice (from £150; www.firstchoice.co.uk), from seven UK regional airports.

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