Picture a typical municipal outdoors swimming pool: children screaming for joy as they zoom down the water slides and plunge into the water. Except, in this case, my children were screaming because they were freezing cold, with a bitter wind whipping the steam off the water and snapping around their ankles as they ran up the steps. Next point: the pools they were plunging into were 41C. The setting was equally surreal. On one side was an alpine-lookalike mountain, and on the other lay a perilously rough sea, the whole scene illuminated by an icy light.
We were enjoying this cold-hot swimming in a pretty little town called Borgarnes, about an hour's drive from Reykjavik, during a late-spring holiday in western Iceland last year. We'd started off at the Hilton Reykjavik Nordica, a sleek establishment where we were introduced to chef Gunnar Karl Gislason's take on Icelandic food. The quality of the cooking is up there with the best London has to offer – dishes such as confit of Icelandic duckling with creamed kale and smoked pork belly should help you get the picture. A day spent exploring Reykjavik was fun: after a sulphurous dip in the nearby geothermal spa that is the famous Blue Lagoon, we window-shopped (Icelandic prices are sky-high) at the retro interior and clothes emporiums on the main shopping street, Laugavegur.
But the children were keen to get out and explore the countryside. OK, that's a lie. Ella, 13, wanted to chat up boys, Milo, 11, wanted to play computer games and Saskia, 8, wanted to set off the hotel fire extinguishers – but we wanted them to explore the countryside. So the next day we drove out to The Glymur, a boutique hotel on the edge of an old whaling fjord, Hvalfjordur. As we drove, the unblemished landscape revealed lava fields, geysers, snow-capped mountains.
The Glymur is the creation of Hansina Einarsdottir, who kept us busy with a visit to the waterfalls at Hraunfossar (keep a tight hold of your children) and a scramble up the dormant volcano at Grabrok (watch you don't get blown over the edge). Everywhere, the weather is extreme: expect to see rainbows, thunder, lightning, rain, hail, snow and sun all at the same time under the huge skies – skies that are still disconcertingly light at 2am.
Yet it was when we arrived at the fishing village of Grundarfjordur, halfway along the northern coast of the Snaefellsnes Peninsula, that we felt we were seeing the real Iceland. We spent a night at the Hotel Framnes, run by ex-fisherman Gisli Olafsson, who set up the hotel in anticipation of the one million tourists expected in the country by 2020. Over a supper of super-fresh fish, Gisli admitted, "I don't want mass tourism to happen, but I know it's going to."
The next day, we drove through the National Park in the Snaefellsnes Peninsula. The Iceland we had seen up until now was harshly beautiful, sometimes even forbidding. Perhaps it was because the sun was shining, but the Snaefellsnes Peninsula had an enchanting quality that seemed different from anywhere else we'd been. It's dominated by the Snaefellsjokull glacier, underneath which bubbles an active volcano. Its beauty has earnt it a place in Icelandic iconography, as well as being the reason Jules Verne chose it as the location for the doorway used by his characters to travel into inner space in Journey to the Centre of the Earth. The glacier is reckoned to be one of the seven points of energy in the world. New-age nonsense or true force of nature – who can tell? But as we enjoyed lunch in the sunshine on the terrace of Fjorhusio, a tiny restaurant overlooking the sea at Hellnar, we all felt pretty happy.
With horse riding and seal watching planned for the afternoon, there was a good chance that the benign mood would linger. At Lysuholl, the children got wet as they made their tough Icelandic ponies run much too fast through streams along the beach next to the crashing waves. Then on to the beach at Ytri-Tunga, where they calmed down a bit and played on the rocks, watching three seals playing in the water, watching the children watching them.
Icelandic Tourist Board (www.visit iceland.com); Icelandair one-way flights to Reykjavik from £80 from London Heathrow; Hilton Reykjavik Nordica: www.hilton.co.uk/reykjavik; Hotel Glymur: www.hotelglymur.is; Hotel Framnes (00 354) 438 6893