The lobby at Fazenda Nova Photograph: Ed Reeve

For years they dreamed of selling up and moving to a place they considered a glorious secret: the eastern Algarve. Hallie and Tim Robinson, from London, viewed it as one of the world's hidden gems – a place of salt pans and sand dunes, vast white beaches, wildlife-filled nature reserves and colourful ferries seemingly taking you back in time to tiny, old-fashioned holiday islands.

Over late-night glasses of wine, they plotted and planned how they would pack up their treasures (the three children – Felix, Milo and Riley) and leave, never to return. But busy jobs, children's schooling and the stress of life got in the way. Hallie worked in fashion PR, while Tim ran a logistics business.

That was until one day early in 2008 when Tim, then 43, suffered a mild heart attack that stopped the family in its tracks. Within six months, the jobs were gone, friends had waved them off and they were in the Algarve, roughing it in the sunshine.

Three years later, they speak Portuguese fluently, their children are in local schools and they have a secluded, 10-bedroom country-house hotel called Fazenda Nova.

Fazenda Nova is 25 minutes by car from Faro airport, and a short drive from Tavira, a town that many Portuguese consider their country's prettiest, dating from the bronze age.

With a magpie eye for flea market knick-knacks and idiosyncratic antique furniture from around the world, the couple have imbued a highly polished modernist interior with their story. Old letterpresses are filled with quirky keyrings and brightly coloured tins wink from the shelves. There are toy robots and glass bottles and old shoes stays, all adding character to the polished concrete and reclaimed wood. Some of their chairs and consoles were Portuguese pieces exported to Brazil during colonisation, which the couple have shipped back

Upstairs in the library are old copies of The Face, Arena and Smash Hits – British cult magazines founded in the 1980s by Nick Logan – Hallie's dad and business partner. Hallie first came to the Algarve as a child with her parents, and says she feels the place has been in her blood ever since.

Delicious fishy tapas at Fazenda Nova

The couple created Fazenda Nova by taking what they saw as the best of old and new: combining original features and traditional Algarve style with contemporary architecture. Family friend David Eyre – founder of London's Eagle gastropub and latterly of the Eyre Brothers restaurant in Shoreditch – has given guidance on the menu, and Kate Lewis, a former chef at the Eagle, works there alongside Ricardo Aragao, who brings years of knowledge of Portuguese cuisine.

The seasonal produce that is served in their restaurant, "A Cozinha", is supplemented by the harvest from their 10 hectares of olive groves, carob, fig and pomegranate orchards and a herb garden.

A 200-year-old bread oven has been restored to working order and is now producing loaves under the watchful eye of local women who know how it should be done.

Nine of the rooms have private gardens or terraces. There's a penthouse suite and two apartments with small kitchens. The infinity pool has views of the surrounding countryside and pod-style hammocks swing under the shade of olive trees.

Tim and Hallie have several favourite places just a short drive away, which they pointed out to me on a map: pretty 18th-century cobblestoned towns, bustling fishing ports and a system of barrier islands – the Ria Formosa – that stretches for 60 miles.

Tim directed me to what he considers his secret haven: the tiny island of Armona. As I stepped off the ferry, I could see the appeal. It is a paradise for those seeking peace, with just a few bars and shops, one-storey bungalows and chalets. There are similar islands and beaches all along this stretch, some accessible by ferry or water taxi. There's also a toytown-style train to the beautiful Praia do Barril beach.

Flea market purchases including vintage magazines

Hallie led me to the place at the top of her list: a flea market, held on the first Sunday of every month beside the beach in the town of Fuseta. It's one of the best I've visited. At one stall, she did the hag

gling for me and for €30 I walked away with a stunning art deco-style crystal chandelier. And of course, she couldn't help buying a few things for herself. Then, turning the corner, we bumped into Hallie's father, bearing a series of vibrant women's magazines from the 1950s. They too were destined for Fazenda Nova.

Célia Pedroso, a Portuguese food writer and friend, took me to the fish and vegetable market in the port town of Olhão where we ogled sardines caught less than an hour previously and stalls of colourful vegetables. We picked the best piri piri peppers, bunches of dried oregano, locally produced honeys and jams, almonds and tinned sardines – all to be stuffed in my suitcase.

On Armona, Célia showed me a trick she learned as a child: digging in the sand with your heels at low tide and collecting dozens of cadelinhas, tiny sweet clams that she later cooked with garlic, coriander and olive oil.

That night, beneath a clear sky, with no light pollution to spoil our view of the endless stars, we sipped at glasses of crisp, slightly gassy vinho verde, and I began plotting my own escape to this secret coast.

• Accommodation was provided by Fazenda Nova (+351 281 961913,fazendanova.eu). Rooms are available from €170 a night. Fazenda Nova is approximately a 25-minute drive from Faro airport. British Airways, easyJet and Monarch fly there from the UK