UK travellers can now travel to Portugal without having to isolate on return. In July, the Government established “travel corridors” with 59 countries, and Portugal has now been added to the list of countries exempt from the mandatory 14-day quarantine. The Foreign Office no longer advises against travelling to the country, nor its autonomous, Atlantic islands, Madeira and the Azores.

Portugal is one of the most popular destinations for UK holidaymakers but has been deprived of one of its biggest markets since the spring. Now is the time to seek out its under-the-radar spots, from the unspoilt beaches of the Alentejo and Algarve to the quiet interior and country’s lush islands.

Alternative Algarve: east and west

With its craggy cliffs and peaceful sands, the Algarve’s wild west is a world away from the busy central coast. Minimalist, four-star Memmo Baleeira perches above the fishing port of Sagres, overlooking the endless golden sands and pounding waves. Guests can rent a bike and sign up for surfing lessons, windsurfing and diving, or simply chill out by the pool and in the spa. Family-friendly suites come with kitchen facilities and sofa beds. Doubles from €110.

The eastern Algarve is within easy reach of Faro, but much quieter than this sun-kissed region’s popular central belt. Check into the sleek Praia Verde Boutique Hotel, which is sandwiched between pine forest and the beach near the historic village of Castro Marim. Every suite has a sitting room with a sofa bed, kitchenette, dining area and balcony, so it’s a good choice for families.

If you tire of the sweeping, powder-soft sands, nearby are the picturesque town of Tavira, whitewashed fishing villages, the wild lagoons of the Ria Formosa National Park or a boat trip down the Guadiana River, which separates Portugal from Spain. Suites from €231 B&B.

A smaller, self-catering option in this tranquil portion of the Algarve is Casa Olhão – a cubist-style two-bedroom house with a pool. It overlooks the region’s biggest fishing port and offers easy access to Ria Formosa’s glorious, white-sand beaches. Sleeping four, it costs from €113 per night.

Digging deeper into the Algarve

North of Sagres, close to neighbouring Alentejo in the Algarve’s interior, Monchique is all verdant hills, cork oaks and quiet villages. The Monchique Resort and Spa makes the most of the mountainous landscape with an abundance of hiking trails and outdoor activities. Doubles from €115.

The region’s extensive network of walking trails include the old pilgrims’ routes of the Rota Vicentina and the inland Via Algarviana, while cyclists will enjoy the 214km coastal trail Ecovia do Litoral. Discover the west’s deserted footpaths, delightful fishing villages and ancient forts on Inntravel’s Algarve’s Coast and Hills self-guided walking package. Guests are based at Quinta das Achadas, a lush country hotel that’s 5km down the road from the pretty fishing port of Lagos. Seven nights from £675pp, including car hire (cyclingwalkingalgarve.pt).

Alentejo’s empty beaches and tranquil walking trails

Sitting above the Algarve, the extensive, cork-forested and vine-streaked Alentejo is blessed with Portugal’s most spectacular coastline and its Atlantic-battered beaches are often empty apart from surfers. Much of the coast is protected as part of the South West Alentejo and Costa Vicentina Natural Park. That means there are no hotels on the beaches, but there are lots of independent guesthouses within easy reach of them, such as charming Cerca do Sul – two white-washed cottages with a small pool, a playground, hammocks and seven cosy rooms. Three nights from €240.

In Santiago do Cacem, on Alentejo’s northern coast, Santiago Hotel Cooking and Nature does exactly that – showcases the region’s bountiful produce and its peaceful, agrarian landscapes. On offer are market visits and foraging trips, a day spent with one of the hotel’s chefs or the chance simply to enjoy the gastronomy – such as lamb stew or acorda (bread soup). Doubles from €121.

Walking and cruising in Alentejo

There are also walking routes to explore, such as the glorious Fisherman’s Way, a pilgrims’ route that winds along clifftops. Pura Aventura’s Alentejo Inn to Inn self-guided tour begins on the Spanish border, and meanders along medieval paths and through fortified hilltop villages and ancient cork forests. It ends at the coast with a section of the Fisherman’s Way and also includes a day in the region’s capital, Evora – a medieval town with 14th-century walls and a Roman temple. Seven nights from £1,455pp, including meals.

Dotted with islets, Alentejo’s Lake Alqueva is the largest artificial lake in Europe, and you can navigate its serene waters by booking a houseboat via Sunvil. Rent a kayak, cycle along the shores or cool off with a dip. At night, lie on deck and admire the twinkling constellations – Alqueva is the world’s first and only Starlight Tourism Destination. A week from £1,345 pp, with flights and car hire.

Head out into the Atlantic

Lying 300 miles off the Moroccan coast, Madeira is a year-round destination thanks to its eternal spring weather and is known as “the floating garden in the Atlantic”. It will soon become clear why if you book a room at the century-old Belmond Reid’s Palace – a five-star clifftop hotel with 10 acres of subtropical gardens. It’s conveniently situated in the island’s capital, Funchal, where pretty squares, museums and excellent shopping await. Five nights from £1,030pp with flights (prestigeholidays.co.uk).

Madeira is criss-crossed by more than 1,300 miles of narrow stone canals and aqueducts, which provide the island with most of its irrigation and some of its loveliest walks. These levadas were dug in the 16th century to funnel rainwater from the mountainous north to the parched south for sugar cane and banana plantations. After a day of exploring, rest your weary feet at Casas de Levada, a bucolic guesthouse with an infinity pool and organic gardens in Ponta de Pargo on the sunny west side of the island. Doubles from €75.

Escape to a remote archipelago

Sunshine is never guaranteed in the Azores – nine, sea-whipped islands flung out in the middle of the Atlantic – but the archipelago’s natural wonders compensate for the odd shower. The chief island, São Miguel, offers azure volcanic lakes, forest-blanketed peaks, geothermal pools and whale-watching. Start your holiday at Solar da Gloria ao Carmo guesthouse, a friendly boutique hotel in a traditional house near the beach and the island’s handsome capital, Ponta Delgada. Doubles from €70.

Only an hour’s drive from Ponta Delgada, the village of Furnas has attracted travellers since Victorian times thanks to its caldera lake and mineral-rich hot springs. Stay at the art deco Terra Nostra Garden Hotel, which is home to one of the island’s best restaurants (local specialities include cozida das furnas, a stew cooked in the steaming ground). The hotel is part of the magical botanical garden of the same name. The centrepiece is a huge bath-warm pool, which guests have exclusive use of in the evenings. Doubles €119.