I walked a selection of this trail but missed out on one of the most beautiful parts in Carinthia. That’s a good enough reason to return to Austria, complete a couple of sections and explore the Lake District.

The Alpe-Adria Trail runs for 750km from the foot of the Grossglockner (at 3,798m Austria’s highest mountain), into Slovenia and ends in Italy, near Trieste on the Adriatic coast.

Lake Millstätter See

I fly into Klagenfurt in the early evening and take a taxi transfer to Millstätt. After around an hour, we crest a ridge and suddenly Lake Millstätter See is spread out below me, hemmed in by high mountains with snow still visible on the distant peaks. At over seven miles long, it’s only Carinthia’s second largest, but is the deepest, plunging to 146m. So clean that they say you can drink it, and it’s crammed with freshwater fish.

The most famous is the Reinanke, belonging to the salmon family, prosaically known in English as White Fish. It entered the lake at the end of the last ice age from the Arctic sea, and people have been eating it ever since.

It fed the Benedictine monks in the Millstatt Monastery and in the 19th century the Bacher family were selected to supply the Imperial court in Vienna. Their descendants still have the right to check their nets every morning and bring in the fish for lunch.

I’m staying right next to lake in the charming See-Villa, and one of a number of country houses built to cater for aristocrats when they started coming here from Vienna in the 19th century.

It has been in the hands of the Tacoli family for the last 40 years and it shows in the efficient way they run it. It has tables at the water’s edge, a delightful opportunity to observe the lake in its many moods. It’s surprisingly warm, since no glacial mountain streams drain into it, and temperatures can reach 25°C in summer. I get into the routine of a daily morning and evening dip.

What they’re promoting here is peace and quiet, with the German slogan Zeit zu zweit, although the English Time for Two doesn’t quite have the same ring to it. If you’re a couple, however, a table for two on a pontoon in the middle of the lake, is a romantic option – each course is delivered by boat.

You can also stay in one of seven Biwaks, scattered around the lake, a sort of luxury bivouac in a wooden shed. Inside there’s a large double bed and windows in the roof so you can observe the stars as you drift into sleep.

An early morning antique rowing boat trip, across to the unspoilt south side of the lake, is an opportunity to admire the fish in the crystal clear waters, with birdsong the only sound.

Motor boats are restricted and you can happily swim across the lake without fear of being mown down. E-biking is also popular and a circuit of the lake is a pleasant way to spend a morning. Being Austria there are plenty on the way offering draught beer, sausage and cheese and, of course, Apple Strudel.

Alpe-Adria Trail

I’m here for sterner stuff and the section of the Alpe-Adria Trail that I missed runs high above the lake on a ridge at 2000m over the Nockberge Mountains. It’s a bit of slog up the road from Seeboden, on the lake, to the Pichlhütte, but then I’m on a grassy path.  The climb continues until I finally reach the summit of Tschiernock, at 2088m, topped with a large cairn and a huge cross. The lake lies below and there are tremendous mountain views right across to the Grossglockner in the far distance.