The sky is clear as I sit sipping coffee in the sunny courtyard of an 18th-century house – now a boutique hotel – in the small Lanzarote town of Teguise. But Óscar Cubillo, my host, sees something different. Looking up, he says: “The planes are always there.

They never stop.” Lanzarote, an island shaped by volcanoes, salt and wind, feels like an otherworldly outpost, but it has recently been wrestling with an influx of tourists that residents fear the island cannot handle. Lanzaroteños are concerned that mass tourism, particularly on the south coast, has driven up house prices and caused environmental damage.

Earlier this year, tens of thousands of protesters marched at rallies across the Canary Islands demanding a rethink of the mass tourism model that has been a mainstay of the archipelago for decades. Their slogan? Canarias tiene un límite – the Canaries have a limit. The protesters were careful to point out that they aren’t against all tourism – they just want limits on its growth.

Cubillo, who hails from the neighbouring island of Tenerife, is committed to a smaller-scale, more sustainable approach. Several years ago, while living in Madrid, he and his partner, designer Gigi de Vidal, came looking for an apartment in Teguise, a village off the beaten track in north-central Lanzarote. Cubillo had fond memories of visiting his grandmother there when he was a child.

Instead of buying a getaway apartment, however, de Vidal and Cubillo found a grand old ho.