ALTHOUGH it has played a vital and glorious role in the history of Europe for four centuries, the elegant city of Vienna has never been as easy to visit as it is now.

With Aer Lingus battling fiercely with easyJet, and the nationalised carriers Austrian Airlines and BA determined to stay in the game, single fares from Gatwick sunk below £10 this year.

What a fantastic invitation to one of Europe’s most elegant and historic cities.

I have yearned to go there, and the 60th anniversary of The Third Man, the famous Carol Reed film starring Orson Welles as Harry Lime, was an obvious time to do so.

I love vintage movies, and never fail to be amazed by the large number of 1920s and ’30s stage operettas and films which glamourised Vienna when it was capital of the Austro-Hungarian empire that crumbled in 1918.

The most evocative of these was Goodnight Vienna, a 1932 film starring Anna Neagle and Jack Buchanan. But night really did fall on Vienna six years later, when Hitler annexed Austria in 1938 to bring Nazi domination and terror to the city.

In 1944-45 it was repeatedly bombed by the Allies. Then, like Berlin, it was subjected to the four-power Allied occupation and turned into an island in a sea of Soviet-controlled territory.

In 1955 Austria became an independent democracy, committed to neutrality, and soon recovered from its travails. War-damaged architectural treasures in Vienna were expertly restored.

I was curious to see how much of the old-fashioned romance still survived – and slightly fearful that globalisation, mass tourism and modern architecture might have stripped away much of its pre-war charm.

Modern-day Vienna works pretty efficiently. After a flight of less than two hours, a fast train whisked me into the city.

When you get there, remember to buy the very useful 72-hour Vienna Card for 18.50 euros (£16.60).

This provides unlimited free travel by underground, bus and tram plus 210 discounts at museums, sights, theatres, concerts, shops and restaurants.

As I avoid taxis on principle, I navigated the city’s underground system, which can be complex. Viennese people are generally helpful – all spoke some English and I can manage basic German – but it took a while to reach my destination.

This was Das Tyrol, a small luxury hotel conveniently situated just off the main shopping street, the Mariahilferstrasse, and almost next door to the Museum Quarter with its beautiful old buildings and art galleries.

My small but comfortable room, with its film-star bathroom, had striking modern decor and proved completely soundproof – a rare luxury in hotels.

The hotel serves an excellent breakfast and gives courteous, efficient service. It is one of the best small hotels I have stayed in.

For a day of sightseeing, I had a personal English-speaking Austrian guide in order to learn far more than if I had been on my own or gone around in a group.

To my delight, I found that my guide, Gerhard Strassgschwandtner, is the creator of an amazing museum in Vienna about The Third Man, which was filmed during the Allied occupation.

Our walking tour through the old city centre gave me a closer look at the buildings near the Museum Quarter, which captivated me when I went exploring on that first evening.

This part of the city, including the former royal stables to the nearby Hofburg Imperial Palace, has been converted into one of the world’s largest museum complexes.

Our visit to the Museum of Fine Arts, commissioned by the Habsburg royal family to house their collections, was a highlight of my trip. I could have spent an entire day there. The building’s magnificent interior is a baroque work of art, and its collection of paintings one of the finest in the world with works by Raphael, Rubens, Rembrandt, Vermeer, Velazquez, Titian and Durer – and the largest batch of Bruegels anywhere in the world.

The 600-year-old Habsburg dynasty’s contribution to the arts, culture and sciences was great, and their architectural heritage lives on in Vienna.

I found that most of the exquisite stuccoed buildings are not as old as they appear, but the result of a massive rebuilding of Vienna in the mid-19th century, a project directed by Emperor Franz Josef.

We walked on to the imposing former Hofburg Palace – the winter home of the Habsburgs – and beautiful St Stephen’s Cathedral, with parts dating to the 12th century.

For lunch at the famous Café Mozart near the Opera, I tried a traditional Viennese dish.

Gerhard suggested Tafelspitz – described in my recipe book as “a fine-fibred, well-hung piece of beef from the rump of a young ox which is boiled until tender. It is served sliced, with chive sauce, horseradish dumpling-bread sauce, apple-horseradish sauce, vegetables and potato rosti”.

I couldn’t put it better myself. It looked a little daunting, with thick slices of greyish meat in a bowl, floating in a clear gravy alongside ox bones, but the meal was delicious, with beef so tender that it virtually melted in my mouth.

Reasonable enough at 19.89 euros, roughly £18 at the current exchange rate.

After lunch I visited Gerard’s museum of fascinating Third Man memorabilia, which started off as his personal collection but grew so large that he opened it to the public a few years ago.

Several generations have been intrigued by this iconic film, in which American racketeer Harry Lime gets his comeuppance while fleeing police through the sewers.

Its haunting theme music was played by a Viennese man, Anton Karas, on a stringed device called a zither, and the original instrument is one of the museum's exhibits along with posters, cinema programs from more than 30 countries, 90 different editions of the novella by Graham Greene on which his screenplay was based, and photographs of occupied Vienna and the making of the movie.

Gerhard also took me into a gloomy sewer that featured in it – a dramatic, if odiferous, experience. Apparently Viennese folk are not great fans of the film, because the city looks so bashed about by the rigours of war.

The transformation in so many areas since then is impressive. Around the museum in Naschmarkt, the seedy buildings of Greene’s day have given way to elegant cafés and smart fruit-and-veg stalls.

It’s easy to fill a few days in Vienna: take the subway to Prater Park to see the Ferris wheel, watch the proud Lippizaner horses of the Spanish Riding School and catch a concert in the opera house.

Next time I will stay longer. Despite those turbulent years of the 20th century, Vienna’s legendary romantic charms are as alluring as ever.