The state visit by George Bush to Britain reminded us above all that our head of state is not Tony Blair, who we elected, but an unelected horse-riding pensioner who drinks Earl Grey, feeds toast to her dogs under the breakfast table, and has her cereal served in Tupperware boxes.

The uncomfortable truth for us sophisticated Brits is that this drawling Texan George W Bush is the head of a democratic state which, for all its faults, was forged in democratic revolution, and built on the enlightenment ideals of equality and liberty. The United Kingdom, in contrast, is a stunted, half-finished democracy with a foot still firmly planted in feudalism, and the overt trappings of a Gilbert and Sullivan comic opera.

The current discussion about the future of the monarchy is disappointingly vapid. Instead of endless speculation about royal flings, finances and frocks, we need a measured and rational national debate about the future of the monarchy. This national conversation should be rooted in the idea that if Britain is to grow up as a democracy, and become a modern European state, we cannot leave the most powerful symbol of our feudal past untouched.

So what shape should this debate take? First, we need to take royal reform in the broader context of changes to society - the collapse of trust in and deference towards traditional institutions, the relentless scrutiny of a 24-hour media, and the changes to the governance of Britain since 1997. Second, we need to establish a democratic principle to guide our reforms. The royal prerogative, used by successive prime ministers to act without reference to parliament, must be reformed so that most decisions are discussed by MPs.

The financing of the royals should be brought under democratic scrutiny. There should be a new definition of a working royal, complete with job description and list of duties, paid for by the state, and the flipside should be a private status for a member of the royal family that involves no state funding.

There should be a debate about the establishment of the Church of England, leading to disestablishment and a separation of church and state. The role of monarch as head of the Commonwealth should be reviewed. The massive royal collection of artworks should be dusted off and brought forward for public view - perhaps on loan to local libraries, hospitals and colleges. More of the royal palaces should be open to the public, on the model of Buckingham palace. These kinds of reform - the constitutional and the symbolic - would create a monarchy more palatable in a modern age, and thus more likely to survive. It would help us as a nation break free from the prison of tradition and pageant.

It is vital that this debate is led by ministers - because ultimately the only way to reform the monarchy is through legislation in parliament. It cannot be left to the tabloids. If we want to join the USA, France, Germany and the rest in the family of democratic nations, we need to take seriously our rhetoric about democracy and become one ourselves.