One of the great trivia facts, on a par with knowing that the collective noun for otters is a romp, or that it is illegal to whistle in London’s Burlington Arcade, is the 12th century law which designates wild swans as belonging to the Queen. It is one of those anachronisms which some would say makes Britain distinctively British.

It doesn’t seem, on the face of it, to do much harm. No one has been on demonstrations against it. But now it is close to being swept into the dustbin of history.

Gordon Brown’s constitutional reform proposals, currently out for consultation, include a pledge to review all elements of the royal prerogative.

When the plans were announced by Jack Straw only days after the handover of power in Downing Street, media coverage focused, quite reasonably, on the move by the government to surrender to MPs its powers to declare war and dissolve parliament.

Yet the green paper, The Governance of Britain, also promises consideration of ‘whether certain prerogative powers, many of which may now be considered archaic, might be transferred elsewhere or even abolished’.

The Ministry of Justice concedes, when pressed, that the list of archaic powers which may face the chop includes the Queen’s ownership of swans, as well as her entitlement to claim all ‘royal fish’ – sturgeon, dolphins, porpoises and whales – caught in British waters.

Indeed, sources tell me that the green paper was at one stage going to make an explicit reference to the question of swans. The relevant section was dropped at the last minute, no doubt for fear that the trivial matter of swans might distract press attention away from the worthy, but slightly anoraky, issue of rebalancing power between executive and legislature.

Yet I think swans are important. If Brown wants to be a modernising prime minister, what better symbol than the sweeping-away of a feudal relic which carries with it an annual ritual of medieval tomfoolery: the Swan Upping ceremony on the Thames, in which royal officials row up the Thames in scarlet uniforms catching and marking swans.

Stripping Her Majesty of the title of ‘Seigneur of the Swans’ would save a few pounds, and push back privilege a notch. Even the swans might be pleased; no one has asked them if they want to be caught. Participants claim that Upping helps deal with sick or injured birds, but if it was that worthwhile surely it would happen on other rivers besides the Thames?

On the very first occasion when I had the chance to subject newspaper readers to my opinions, I used the opportunity to call for the scrapping of academic gowns, on the grounds that they cause hidden harm by dividing students from townsfolk.

Traditions may be old and colourful, but that does not mean they should carry on forever. I hope the government sticks to its guns over the royal prerogative. In the words of the prime minister, let the work of change begin.

The Cabinet Office has been mocked in some quarters for carrying out a consultation on how the government should carry out consultations.

Yet once you get over the ‘Yes Minister-ish’ concept, this is rather important. Consultations have long been abused in Whitehall as a figleaf for decisions that have already been taken, or as a stalling tactic. Cynicism is so great that if a minister consults, listens, and changes his or her mind, they will be accused of using the consultation as an excuse for a U-turn.

I have recently responded to two government consultations, one on freedom of information and the other on secrecy in family courts. Few people knew about them, the questions seemed slanted and closed-ended, and I was certain that my replies would be ignored.

Yet as I posted back my forms, I felt a great sense of involvement. Why not promote consultations better, and give the thousands who sign petitions on the Downing Street website a voice in formal policy-making?