A rock star could provide as much glamour as a prince

I once went to a party, given by someone I didn't really know, for no better reason than this: Martine McCutcheon was going to be there. Now famous for selling yoghurt, Miss McCutcheon had just finished playing Tiffany on EastEnders and was heading for star roles in an ill-fated My Fair Lady and Richard Curtis's Love Actually. I couldn't wait.

Fantasies of bonding with this glamorous figure over the canapés filled my mind all week. Of course, I went, and glimpsed her without exchanging a word. I talked to acquaintances about what they were up to, and what I was up to, and all of that. But for the next month I bored everyone with this incredible fact: I went to a party with Martine McCutcheon at it.

Plenty of people have considered that this frankly vulgar motive in human behaviour ought to be harnessed for public gain. Some celebrities, for instance, hire themselves out to nightclubs and parties for a fee, so that the gawping public can say that they have been in the same room as the starlet of the moment. The business does a roaring trade on the night, and hopes that the punters will turn up next week, minus the celebrity. Sometimes, it even works.

This, surely, is the explanation for Prince Andrew. He acts as a "trade envoy" for the UK, travelling abroad to drum up business. In social events across the world, he shakes hands with local businessmen; he makes speeches commending UK exports; he smiles and exchanges manly jokes. He has held the post of UK "Special Representative for Trade and Investment" since 2001.

Faintly disreputable stories about the Duke of York have been circulating for years. One diplomat who had to deal with him on an official visit complained about "a number of schoolboy jokes by the Prince. He even suggested that my wife had 'touched him up' under the table". Everyone knows the Royal Family has a somewhat broad sense of humour, but tales of rudeness on official outings amassed in large numbers – snubbing important partners, skipping off early from embassy receptions to go to private parties, leading forth on subjects in company and refusing to listen when the better-informed disagreed.

There have, too, been suggestions over the years that personal gain played a part in some of these overseas trips. Questions have been raised over the sale of his Ascot house in 2007 to the son-in-law of the President of Kazakhstan for £3m more than the asking price. That same diplomat claimed that "on a visit to the Gulf in 2005, Prince Andrew was hawking this house around during meetings with Gulf royals. Indeed, his private secretary" – a public official, after all – "had sounded people out about it in advance on a recce visit".

On the whole, we have been putting up with this, and with the extraordinary style in which Prince Andrew carries out his role, for one reason: he is the second son of the Queen, and fourth in line to the throne. We don't see anything so very strange in the idea that someone in this role should travel around by private jet with valets and equerries and private secretaries and bodyguards; that, famously, his valet brings his own ironing board with him everywhere he goes, because he has been touched, fairly remotely, by the Divine Right of Kings. There are other pieces of curious behaviour elsewhere in the Royal Family; one, I understand, employs a member of staff to carry around a white leather toilet-seat cover; another asks hosts to cut up food in advance; the Prince of Wales requires his valet to squeeze toothpaste on to his toothbrush. The whims of rich men are harmless, and none of our business. But the Duke of York's behaviour abroad in a quasi-official role, representing Britain, very much is our concern.

Questions about this particular member of the Royal Family have been increasing in numbers in recent months. The WikiLeaks exposure of diplomatic cables included an interesting one from the US ambassador to Kyrgyzstan, Tatiana Gfoeller, in which she described a brunch there attended by the Duke. He complained about anti-corruption investigators scuttling arms deals; about journalists seeking transparency; about the innate honesty of the French; and, weirdly, about American geography teachers – "The Americans don't understand geography. Never have. In the UK, we have the best geography teachers in the world!"

Since then, attention has been paid to a number of the Duke's business contacts. They are not all that one might hope. The son-in-law of the deposed Tunisian dictator, Zine al-Abedine ben Ali, was invited by the Duke to lunch at Buckingham Palace a mere three months before the regime was toppled. It is true that royalty sometimes has to entertain some unappealing people – even the Queen entertained Ceasescu, after all. But then another dubious friend appeared; an American billionaire called Jeffrey Epstein, who has served a prison sentence for soliciting an underage girl for prostitution. The Duke was photographed with his arm round one of Epstein's teenage girls. Members of the Government have quickly been at pains to point out that the Duke is, in his role, nothing more than "a volunteer"; other politicians have used the words "an embarrassment".

The fact that matters have got this far before politicians are prepared to say that enough is enough is truly startling. What a Duke of York can offer trade missions is not informed views, or gracious behaviour, but just one thing: a high RSVP response. The punters will turn up to a garden party with an HRH when a mere KCMG can't work his magic. Perhaps, too, those Kyrgyzstan-based businessmen considered that they had got their money's worth with those impressive golf-club opinions, particularly since they shocked an impressionable US ambassador.

But the element that attracts the punters – the combination of snobbery and freakshow – is not possessed these days exclusively by royalty. The time may be coming where foreign missions conclude that a bigger box-office draw for the garden parties may be provided by an English Oscar-winner, a rock star, or perhaps even a bearded lady – you never know. Perhaps Miss Martine McCutcheon wouldn't work the same magic in Kyrgyzstan, even if she were persuaded to insult an American geography teacher or two. But the time is coming when Prince Andrew's devotion to golf and getting his shirts perfectly ironed on his own ironing board can usefully be pursued in his own time, in private.