Thick grey-green mud squidges through my toes as I step into the icy, irresistible water. I’m on the descent from the Britannia Hut at the foot of the Allalinhorn in the Valais canton of the Swiss Alps, and this turquoise pool of glacial meltwater has been on the horizon tempting me for an hour. I peel off all five layers of clothing and plunge into the murky water. After a night in a shared dorm without showers it’s bliss.

In winter, the jagged ridges of the Valais are the domain of expert skiers and ice climbers, but in summer the lower slopes become accessible to hikers, with the added bonus of the ski lift infrastructure. You can be surrounded by dramatic peaks with the security of well-marked trails ranging from gentle strolls to serious alpine routes. I’m here to hike to mountain huts, test my nerves on via ferrata routes, and fill my city-dweller lungs with clean Alpine air.

I begin my trip in Saas-Fee, a car-free high altitude village in the south-west of Switzerland, where I spend the night at the Walliserhof Grand-Hotel, famous for hosting Wham! when they filmed the Last Christmas music video here. From my balcony with a cold beer, I spend the evening drinking in views of church spires, geranium-covered balconies and the towering wall of mountains beyond.

Between Saas-Fee and the village of Saas-Grund lies a deep gorge – the Sass-Fee Alpine Canyon – which can only be tackled with a guide. A via ferrata system of ladders, metal rungs and cables allows climbers to access high-level routes while clipped into a safety cable. I’m lucky to be assigned Aldo Lomatter as my guide the next morning – he built this canyon route and knows it better than anyone. We criss-cross the gorge on wobbly bridges, climb ladders up and down the rock face, and disappear into gulleys on ziplines.

The intensity of the challenges build as the route progresses: crossing high above the river a vertiginous ladder bridge abruptly stops, and it’s a 40-metre abseil to the riverbed. We finish with a zipline, which ends deep in a dark cave: it’s a leap of faith, but also the only way down – and a thrilling finale. Climbing out of the cave on a shaky ladder, I emerge blinking into the sunlit hamlet of Saas-Grund and take the free minibus back to Saas-Fee for a fondue lunch.

Suitably refuelled, it’s time for my next adventure: a gondola and cable car take me to Morenia, the top gondola station, for the walk to the Britannia Hut at 3,030 metres. Only reachable by foot or helicopter, it’s a gentle two-hour hike over Egginerjoch but, even in mid-summer, much of that is over snow – though thankfully no crampons are needed.

The hut was built in 1912 as a gift from British members of the Swiss Alpine Club to thank the Swiss for their hospitality in the mountains. From the deckchairs outside, the views over the Allalin glacier and the Mattmark area are jaw-dropping.

Accommodation is simple but practical. Hikers share dormitories with wide wooden bunks, ours sleeps eight. There are communal plastic clogs to give tired feet a break from walking boots, otherwise guests pad around in thermals and big jumpers. The tap water isn’t drinkable and there are no showers. Supplies are brought up by helicopter, and water is as expensive as beer. Dinner is one sitting at 7pm, served family style with all guests eating the same meal. It’s hearty mountain food: cream of vegetable soup, saffron risotto, roast beef, vegetables and a fruit pudding. Hiking tales and weather forecasts are swapped jovially in many languages around the table. I sleep soundly, though I’m grateful for my earplugs and eye mask. Many guests here are preparing for long days and distant summits, so breakfast is served at 3am, 5am or 7am, and by the time I turn up for the last sitting the hut has mostly emptied.

I retrace my route to Morenia, stopping to cool off in meltwater on the way, and take the gondola back down to Saas-Fee where a second dip awaits at the WellnessHostel 4000, a youth hostel with its own spa. Below the cafeteria and dormitories, there are a 25-metre swimming pool and elegant wood-panelled, adults-only spa overlooking the gorge I traversed days before. I buy a day pass (CHF34.40) and spend a leisurely few hours in the pool, saunas and steam rooms, gazing out at the trees and river below. After a day in the mountains it’s a wonderful way to stretch tired muscles.

Keen to explore the area further, I take the free PostBus down the mountain to Visp and catch a train to Champéry at the other end of the canton. I spend a night at traditional family-run Hôtel Suisse, and eat at Café du Nord sitting outside under a fairy-light canopy. The next morning I meet Lloyd Wiltshire from Experience Champéry to be fitted with a harness for my next vertiginous challenge, Champéry’s Tière via ferrata, which takes climbers up steep cliffs high above the valley and is reached by a winding uphill walk through woods dripping with lichen. The most challenging point is a tricky climb in the spray of a thundering waterfall, followed by a single wire crossing above the River Tière – not for the faint-hearted.

After lunch I take the Croix de Culet cable car from Champéry to 1,962 metres. Covered in lush grass and alpine flowers, it’s hard to imagine that this is a popular ski area in winter. I walk through farmland, stopping to buy freshly made cheese and cakes from simple cafes and honesty boxes. My summit today is the Col de Cou mountain pass, where I stand with a foot either side of the French-Swiss border looking over the Terres Maudites and the Manche valley in France, and the Dents du Midi and Dents Blanches ridges in Switzerland.

Descending to the tranquil Barme plateau with tired legs, I find rest and refuge at Cantine de Barmaz, a rural restaurant with rooms. On the menu, the house special is choléra, a deliciously hearty leek, potato and cheese pie, ideal post-hike fortification with a glass of cold Swiss wine. I watch as the last light of the day illuminates the jagged spikes of the Dents du Midi in shades of glorious umber and gold. I then cosy into my dormitory bed in the eaves, lulled to sleep by the deep breathing of tired hikers and the rhythmic clang of distant cowbells.

The trip was provided by Saas-Fee Saastal, Région Dents du Midi and Visit Switzerland. For more information on the region see valais.ch. Half-board at Britannia Hut costs CHF98 (£92) a night for non-SAC members (CHF84 for members). Half-board at Auberge de montagne Cantine de Barmaz costs CHF68 a night in a dorm or CHF75 in a private room