One Thursday lunchtime in March every year, a surprising sight can be seen in a warehouse-like building in the Dutch town of Maastricht. Hundreds of well-groomed men and beautifully dressed women are standing about drinking claret or champagne. They have come from all over Europe, the United States, the Middle East and China. This year, a hundred and twenty-five private jets were counted bringing visitors to the little Maastricht-Aachen airport for the event.

It is not a tremendous libation to forthcoming bank bonuses (though many bankers are undoubtedly there). It is the opening day of an eleven-day art fair, with the ugly but now accepted name of TEFAF – The European Fine Arts Fair – and two hundred and sixty dealers are waiting on their stands with their wares. I asked a friend of mine if there was any equivalent gathering in Britain. ‘Yes,’ she said, ‘this is Ascot – but with pictures not ponies in the paddock.’

Maastricht is of course most famous nowadays as the place where the treaty creating the European Union was signed. But do not come here to look at the building where the signatories assembled. Though it has a commanding position on the bank of the broad River Maas, it is the dullest possible set of brick municipal offices.

Better to visit the old town on the nearby hillside, with its narrow cobbled streets and its vast, dark twelfth-century church of Onze Lieve Vrouwe – Our Dear Lady – which is a fortress, with loopholes for arrows as well as fine stained glass windows, around which the wars of Europe raged.

By contrast, the post-war district on the other side of the river where TEFAF is held is not just dull, it is hideous – a group of enormous, characterless sheds by contemporary architects. How did that elegant people, the Dutch, manage to do it?

But step inside the TEFAF shed, and in an instant you are in a world of luxe, calme et volupté. You walk down a long corridor flanked by walls covered with fresh red carnations. In the distance you seem to glimpse a glittering meadow by Renoir, a tambourine with a funny Picasso face on it – and surely that must be a pre-Christian Egyptian bronze goose over there! Then, on the first day, the scene I have described opens out before you. It is especially luxurious on that first day when the visitors are all guests – wealthy connoisseurs invited by the dealers, powerful museum directors and curators, government ministers and local mayors. But it is not very different on subsequent days – only the champagne and claret are no longer free, and you have to pay to get in.

In some ways that first impression is an illusion. Work is going on here. The waiting art dealers have a hard week ahead of them. Try to engage one of them at his stand in light-hearted conversation and you will get a very cold shoulder. In that moment he may lose a customer – a visitor who had stopped to look at a picture but has now moved on to the next stand. Large sums are at stake. That picture that seemed to be a Renoir was indeed a Renoir – a girl who had dropped her parasol among the flowers – and its asking price was fifteen million dollars.

Many of the drinkers will also be working hard, though their manner, like that of the dealers, will be carefully suave. A museum curator with a strictly limited cheque book may be hoping to pull off the purchase of that little Boudin painting that will fill the gap in the collection – and it may take some cool bargaining. (This year there were a hundred and forty- two curators at the fair, including thirty-eight from Germany and twelve from Britain.) A connoisseur hoping to make a good profit is searching for just that little view of Delft that he will know more about than the dealer. Some visitors may have someone with them who is hard to please. This year there was a yellow diamond called the Delaire Sunrise on sale for eighteen million euros. I heard a young woman say: ‘But darling, I don’t like yellow.’

Maastricht has always been a fair for valuable, older works of art, especially paintings, and there are always many masterpieces to be seen, from (to take this year) a Cranach Virgin and Child formerly owned by the Grand Duke of Sachsen-Weimar-Eisenbach (2.9 million euros) to an old, white-bearded man by Jan Lievens (3.9 million euros). Then there is furniture – last year, a French Empire bed slept in by Talleyrand, this year a Napoleonic campaign chair in steel and leather that could have been designed by Terence Conran. But everyone acknowledges that the supply of monumental Old Masters to the market is fast drying up. Almost all of them now are in museums and, short of a cataclysm, will never be sold again.

In recent years contemporary art has had a presence, though a shaky one, at the fair. Five years ago even the most staid dealers seemed to have hung up some Damien Hirst coloured spots behind their Roman busts or cabinets of Japanese netsuke. This year some of the main specialists in contemporary art had gone from the fair. One of those was the Gagosian gallery, which was so haughty that all the items on its stand were unlabelled. The message was that if you did not know who the artist was you had no right being there.

For the visitor to the fair who comes not to buy but just to look the fair is always an overwhelming experience. Where will you go among the broad corridors with names like Rembrandt Plein and Sunset Boulevard? Which stands will you stop at? What works will you linger over? What you must do is let your eye lead you. There is a lovely little Utrillo of Montmartre! There – good gracious – is a wall of Rembrandt etchings! There is a little ring of Miro sculptures – you had not realised before that he was a sculptor too! It is overwhelming – but it is wonderful.

However, you may have a little trouble getting to the fair. The Netherlands adores TEFAF – but it does not seem as if Belgium feels the same. If you take Eurostar to Brussels and then change to a Belgian train to Maastricht, you may get a shock.

The evening that I went, the Wednesday before the opening, the train that I was on stopped at the little frontier town of Vise, and everybody was told to get off. We were only about ten miles from Maastricht, the train’s last stop, on the other side of the border. But the train was turning round. If it did not, it would be late for all the Belgian commuters back along the line who were going home to Brussels. Passengers for Maastricht would have to wait for another train, or fend for themselves.

I was left on the platform with a crowd of frantic dealers who had dinner dates in Maastricht and were phoning madly for taxis. Fortunately, one of those took me along. Better perhaps, like so many of the other visitors, just to have taken the private jet.