So there we were, shades on, hair bleached by the sun, kicking back with a few cold ones in the beach-front bar, swapping gnarly surfer tales with the gnarly surfer dudes, as the waves crashed against the sand below and a vast blood-orange sun began its spectacular slow-dive into the wild Atlantic beyond.
Not bad, we agreed, for a first day's bodyboarding, especially when – like Eliza and Gabriel – you're five and seven and the closest you've been to really big waves before was at the Brentford Leisure Centre.
We'd come to the Algarve to look for another side of Portugal's most popular holiday destination. For us, the area's traditional image – of men and women of a certain age hurtling on battery-powered buggies between the bunkers of innumerable faceless "golf resorts" – was about as attractive as a warm bottle of Mateus Rosé. But as we suspected, the secret of a great holiday in The Algarve turned out to be not actually to go to "The Algarve" at all – or at least, to avoid that slim strip of touristic development, stretching like a ribbon along the sheltered south coast.
Instead, we decided to base ourselves a little way inland, finding a stylish modern villa, A Senora da Montanha, an easy drive into the hills of the Serra de Monchique, which mark the Algarve's mountainous northern boundary. Here, a few hundred feet up, amid groves of acacia, cork and pine, you enter a different world: the air is cooler, with gentle breezes bringing relief from summer heat, and you can look down – literally – on the sweltering masses below.
The view from our terrace was simply breathtaking, falling away 20km to the sea – lights twinkling at night in the distance, but with somehow hardly another house in sight. Within a few metres of our door, the children found peaches, avocados, figs, grapes, dates, limes, pears, lemons, plums and olives – and probably missed a few more. And as the grown-ups relaxed in the garden at the end of the day, a cool glass of vinho verde in hand, the loudest noises we could hear were the tinkling bells of goats snuffling in the orchards below. Heaven, we thought, must be like this.
The temptation up here is not to do anything, beyond taking the occasional stroll or splashing in the pool. But even without visiting the fleshpots of Albufeira and Praia da Rocha, we found plenty to draw us away. We frolicked by the fountains at the historic spa of Caldas de Monchique; we ate lip-smackingly good piri-piri chicken at unmarked roadside cafés; we strolled through the charming hill town of Monchique itself, stopping to sample the local firewater, distilled from berries of the arbutus, or strawberry tree.
And, of course, we hit the surf – driving along the Serra's spine to reach the wilder west-coast beaches of Amado, Castelejo and our favourite, Arifana. As you descend to the coast, the landscape takes on a truly Atlantic character – as if the rugged headlands and golden sands of Cornwall and Devon had been transported to this remote spot under the hot Portuguese sun. Here is one of Europe's undiscovered treasures – thankfully protected by a 120km-long Parque Natural, which helps ensure that "tourist development" mostly means a café in a shack by the beach. It all feels like a fabulous secret, shared only by the intrepid few who make it this far. Their reward? Having miles and miles of these dramatic beaches (almost) to themselves.
If truth be told, our adventures were tame compared to those of the real surfers who come here to ride some of Europe's most challenging waves. But the excitement of discovering this coast for ourselves was genuine indeed. And as we loaded up the children to drive back through the gathering darkness to our magical hillside retreat, where another bottle of vinho verde was chilling, we reflected: The Algarve without "The Algarve"? We'll be back!
Simply offers seven nights in Portugal, staying at the A Senhora da Montanha from £579 per person. Visit simplytravel.co.uk
# On the southern edge of Dartmoor, and a short drive from Devon's unspoilt beaches, Hoseason's eco-friendly lodges at Indio Lakes offer tranquil, luxurious accommodation. Don't miss feeding the Dartmoor ponies at nearby Becky Falls. A week in March for a family of four from £520; hoseasons.co.uk
# One fail-safe option for the little ones is Fowey Hall, the popular family-friendly hotel overlooking this quaint Cornish fishing village, a stone's throw from the Eden Project. Children and adults alike love an atmosphere that reminds us of a country-house party – with the added bonus of a great pool and spa complex – and it's easy to see why many families return here year after year. Rooms from £130 inc. breakfast. See www.foweyhallhotel.co.uk
# For affordable South of France glamour, take the train to Perpignan and spend a week in a luxury mobile home at Cala Gogo on the beautiful beach at Saint Cyprien. Return fares from London from £109; raileurope.co.uk . Seven nights in a mobile home in May from £269 inc. ferry crossing; keycamp.co.uk
# Or why not take a tour of Bulgaria's lakes and mountains? Try a children's bungee in Sofia, kayak round a reservoir and rock-climb in the Rila Mountains. Plus plenty of time for relaxation around the guesthouse pool. Eight days from £894pp (0844 499 0901; explore.co.uk ).
# Finally, if you're still searching for inspiration, why not do what your children want you to do – and book a trip to one of Center Parcs four UK locations? Whichever you choose, you'll find an unbeatable choice of indoor and outdoor activities, including the weather-defying Subtropical Swimming Paradise. See centerparcs.co.uk