Once an elite resort, Lech is now luring families. But it hasn't lost its luxury or stunning ski runs

Taking a cable-car is becoming just as laborious as catching a plane. First you check in at the ticket scanner; then you join a long queue for those smart turnstiles, which close automatically when a full load of passengers has passed through

Taking a cable-car is becoming just as laborious as catching a plane. First you check in at the ticket scanner; then you join a long queue for those smart turnstiles, which close automatically when a full load of passengers has passed through; penned in the departure lounge, you are released just in time to see the cable-car you missed slowly take off for the mountain-top. Getting up there on a chair-lift might be no quicker, but at least the sight of the never-ending line of empty seats heading down the mountain to pick up passengers makes the waiting easier.

Except in the most inclement weather, the ride is better on a chair-lift, too: you always get a seat, and a good view, rather than having to stand in your allotted square-foot of space with somebody else's ski pressed against your cheek. But there's a pay-off from some cable-car rides, once you get to the top.

I first appreciated this at Tignes, in France, after taking the huge cable-car up to La Grande Motte. The view across the Isère valley from the top station is so impressive, I had to stop and pen a short ode to nature's marvels. When I turned to ski down I was alone: all the other skiers had departed, and the next cable-car was only halfway up the mountain. I had the whole, wide piste to myself.

Last weekend, the Austrian resort of Lech offered a similar treat. The Rüfikopf-Bahn cable-car climbs almost 1,000m from the valley. At the top there is no restaurant or any other distraction; the only thing to delay skiers is the choice between heading back down to Lech or along the valley. Despite a howling gale on the 2,362m ridge, I lingered there until all the others had left and then set off, slowly, along the sawtooth of lifts and descents towards Zürs.

With access to the area provided only by the cable-car, skiers pass so predictably and so infrequently that the operator of the nearest drag-lift saves electricity by turning it on and off. Imagine the sense of luxury. This time I had not just a piste to myself, but a whole, stunning valley face. And here, the lifts were switched on for me when I needed them.

Finding such luxury and solitude is appropriate in Lech, which has long been run on the same sort of principle as the old Brooklands race track: "The right crowd, and no crowding" (although the Lech/Zürs advertising slogan is actually the less evocative "More time, more space"). Lech is a member of the "Best of the Alps" marketing organisation, along with other classic resorts such as Cortina, St Moritz and Zermatt – and, like them, has always had an exclusive, upmarket sheen. And it is renowned for its door policy: when 14,000 people are on the ski area, it is deemed to be full and signs warn drivers coming up the valley road that they will not be able to buy a lift-pass for the 110km of pistes above Lech, Zürs and Zug.

Traditionally the haunt of the rich, famous and occasionally royal, Lech has done a good job of maintaining its traditional custom, attracting at least three generations of Monaco's royal family, and doing so well with repeat business that only 25 per cent of guests have never been there before. But over recent years, it has also extended its appeal.

One only has to look at Jaguar's current TV advertising campaign for its S-type model to see how the desire to broaden the market for a classic product can induce brand panic: although the car still has the upholstered appearance of old Jaguars – and its interior is still like a cigar room – the "owners" portrayed in the advertisement are a couple of twentysomething style-mongers who would rather boil their own heads than be seen in a Jag. Lech has not made the mistake of suddenly claiming it is a radical, nu-skool resort for boarders offering full-on clubbing. Its strategy has been to develop its family-skiing facilities – and thus attract two generations for the price of one. Much of its recent investment has gone into the Oberlech area 200m up the slopes from Lech itself, which provides ski-in, ski-out accommodation, a car-free environment and a system of tunnels beneath the slopes for the passage of guests, their luggage and goods deliveries.

It's not surprising the UK's biggest ski operator, the mid-market, family-oriented Crystal Holidays, chose to introduce Lech in its brochure for this season, nor that the first sitting for lunch at local pizza restaurants is packed with children.

Since this was my first visit, I don't know whether Lech was once an aggressively posh, fur-coat place. It certainly isn't now – although not even Crystal has made it exactly cheap. With 7,000 tourist beds, it is fairly typical of larger Austrian resorts, with good hotels (six of them five-star), excellent service, largely intermediate skiing (plus plenty of off-piste) and an efficient lift system. But, along with the other Arlberg resorts, it has the advantage of a snow-sure ski area: its annual average snowfall is 9m. Enough fell on the area during my visit to make crossing into its narrow valley from the St Anton road alarming on Thursday night of last week, and quite impossible by Monday this week.

If the village is not exceptional apart from its elegant, onion-domed, 14th-century church, its surroundings certainly are. The circuit from the Rüfikopf-Bahn to Zürs, and back along the other side of the valley is one of the great ski journeys, at least for aesthetes – more athletic skiers might prefer the black runs off the other side of the cable-car which, since I was skiing alone in poor light with new boots and unfamiliar skis, I didn't dare tackle.

The whole circuit is surrounded by 2,500m-plus peaks soaring above the narrow valleys, giving the impression of skiing in a huge, complex snow-bowl. True, a few more trees would be nice; but you can't have everything. The low point of the route is at Zürs, where a "moving carpet" – a rubber conveyor belt – is provided on the bridge across the valley road. A warning sign alongside it reads: "No passengers accepted with loose garments, open long hair and anything like it."

This seemed both unnecessarily alarmist, and puzzling. Who, I wondered, could get into trouble on a slow-moving, rubber conveyor? The answer was the man in front of me, who somehow contrived to fall into a tricky position in which his skis were half-on and half-off the belt. And what could the sign mean by "anything like" loose garments and open long hair? The only thing I could think of was a grass skirt.

Crystal Holidays (0870 848 7000, www.crystalski.co.uk) offers late-season packages to Lech from £585 per week half-board, based on two sharing. Other UK tour operators featuring Lech include Inghams, Abercrombie & Kent, Flexiski and White Roc