And Lanzarote deserves to be explored. At first sight the interior looks like a series of vast camel-coloured slag heaps. Get closer to the landscape and you really see nature in the raw.

Less than 300 years ago, massive eruptions spread lava over a big chunk of the island and created more than 20 new mountains. You can drive through this amazing landscape, or even take a camel trek over it.

It looks a hostile environment. But get out of your car and it has a different aspect. We parked more or less at random and followed a track into the hills. There were wild flowers, shrubs and even grass everywhere. We intended to have only a short stroll, but the track was so peaceful and the air so clear that we kept going for two or three miles until, high up on the side of a volcano, where the views were superb, the track petered out.

Another day we headed north to the little port of Orzola – you can catch a ferry from here to Graciosa, the desert island off the northern tip of Lanzarote. But despite the attractions of Graciosa’s beaches, we didn’t catch the boat (it leaves at 10 in the morning).

Instead we took a walk and then lunched at Restaurante Alegranza, an unpretentious place one street back from Orzola’s more crowded (and pricier) seafront eateries.

For €7 each (about a fiver) we had a three-course meal of Canarian stew, superb fish and – well, what do you expect for that price? – a banana. When the bill came, the only extra was a bottle of beer, but we’d polished off three between us. “No – one drink each is included in the price,” said Teo the owner when I pointed out the mistake.

There are set-piece tourist attractions that are worth visiting, including the Jameos del Agua (deep caverns, one of which has been turned into an auditorium) and the volcanic Timanfaya natural park, with those camel tours and a restaurant where meat is grilled by natural heat.

But there are plenty of wonders you don’t have to pay to see. For instance, while the views from the Mirador del Rio (entrance €2.70) across to Graciosa are absolutely stunning, you can get equally impressive free views from the Mirador de Guinate a couple of miles along the coast.

And there’s no charge at El Golfo, where the sea has broken into a volcanic crater, exposing the raw crater wall and leaving a luridly green lake in the black sand.

In fact, almost anywhere you go in Lanzarote you will come across strange and interesting sights, like vineyards where each vine sits within its own circular stone wall, or the practice of spreading black volcanic gravel as a mulch on the fields.

The island’s most spectacular beach is Famara, on the wilder west coast. Backed by cliffs 1,500 feet high, it’s a favourite with wind-surfers. It’s often windy and the big Atlantic rollers mean it’s essential to make sure it’s safe before swimming. If it’s rough there, though, the La Santa sports centre further down the coast has a calm lagoon which, despite appearances, isn’t private.