It is a Bank Holiday Monday. So how about a quick quiz? What, at the last census, was the third most populous city in the United Kingdom? Manchester, maybe, Liverpool, perhaps, I sense you wondering. No, it is Leeds. How about the fourth largest then? It is Glasgow. The fifth, it must be Manchester or Liverpool surely, but it is Sheffield. And finally the sixth.

Just one shot at this. Hard luck. It is Bradford. Liverpool comes in eighth (behind Edinburgh) and Manchester is ninth (ahead of Bristol). I would have put Newcastle in the top ten but Cardiff, Coventry, Leicester, Belfast and Nottingham all outscore it.

If these answers come as a surprise, you could be forgiven. Because, put bluntly, these cities are an irrelevance. There is only one city that truly counts in this country and that is London. It is not just the largest place in the UK but comfortably the biggest in the whole of the EU.

It will retain that status until Turkey, and through it Istanbul, is awarded membership, so (in my view, alas) it is safe for a fair few decades, if not another century. In 2001, London was (at 7.17 million people) seven times larger than the second city of Birmingham (971,000).

Population estimates since then indicate that the margin had expanded to 7.5 by 2006 and could reach a factor of 8 by 2011.

It is rarely appreciated how unusual this situation is. In France, Paris is a mere 2.5 times the size of its nearest rival (Marseilles). In Germany, Berlin is but twice that of Hamburg. In Italy, the ratio between Rome and Milan is 2:1 as well. In Spain, the same applies to Madrid and Barcelona. In Poland, it also the case for Warsaw and Lodz. With the exception of micro-states, it is hard to find any other similar dominance of one city across the rest across Europe. There is, in fairness, a place that is almost the same. Whether, in the light of events, we deem Austria a sound fellow model is debatable.

So we live in what is universally recognised as a highly centralised country that is overwhelmed to an arguably deeply unhealthy extent by one supersized city. To compound this, what is the sole part of England that enjoys a decent element of decentralised authority? London, the conurbation that lords it over every other city, town or village.

The real significance of the mayoral election in the capital on Thursday was not the identity of the winner. In fairness to Boris Johnson, it was an extraordinary triumph. Like many others I could not imagine how he would see through a lengthy campaign without saying something that would sink himself or being found in bed with half the Arsenal Ladies football team (“Cripes. How did this lot get here? Oh. Who cares?”). David Blaine was lauded last week for holding his breath under water for more than 17 minutes. To my mind, Mr Johnson holding his tongue for more than 17 was far more astonishing.

Yet what truly matters is that this was the year when the mayoralty as an institution came of age. It has taken two terms of Ken Livingstone for Londoners to work out what it does, what it is reasonable to ask from it and for it to attract high- profile contenders across the spectrum. The Scottish Parliament needed an equivalent length of time to take root but under Alex Salmond and the SNP it too has unquestionably done so. The turnout in the capital was 45 per cent, staggering by the standards of local elections, and the media coverage was exhaustive. The expectation of the mayor has become that he should be able to cut crime, recast public transport and frame planning practice in his own fashion.

If a directly elected mayor is beneficial for Londoners, why not other British cities? Well, once bedded in they most certainly would be. Tony Blair's original vision was that where London led, the likes of Birmingham and Leeds would wish to follow. It is absolutely vital that they do so. For if they do not, London will be able to exploit its advantage and become even more omnipresent over the nation.

Why have these other cities not adopted mayors? Simple. Vested interests oppose this. Councillors loathe the idea of being marginalised while one single individual exercises a semi-Napoleonic status. MPs are also not that wild about no longer being the king of the castle in their neighbourhoods. It is an irony of London itself that if the GLC had not been curtly abolished by Margaret Thatcher, then it would probably have been impossible for Mr Blair to have created a directly elected mayor as the GLC would have fought fiercely to prevent this new position sidelining it. If it is left to the councils in Britain's other cities, no new mayors will ever emerge.

That is why, paradoxically, if bottom-up local democracy is to be revived here then top-down action is essential. Mayors can only be established today either at the behest of councils (fat chance, in the main) or via a complicated locally inspired referendum. This is too restrictive. It would be better for both Gordon Brown and David Cameron (and Nick Clegg if he is brave, for his party will not much care for it) to acknowledge that the directly elected mayoralty has shown its worth in London and must be duplicated in the 19 next-biggest cities in the country.

It will take a decade before their impact is evident. It is safe to assume that in time they would be catalysts for urban renewal.

Ten years ago, I wrote a pamphlet for the think-tank Politeia, which examined the American experience of elected mayors and concluded that ministers should allow a mayor of London maximum power. One politician condemned the proposal as “virtually fascist”. I wonder whether, in the light of his experience, Mr Livingstone might reconsider his assessment more sympathetically.

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