London has a rich history of financial innovation going back at least as far as Lloyd's coffee house (where the insurance market originated in 1688), and beyond into markets now lost in the mists of time. But it is all very well to invoke the past; London's future prosperity depends on it being able to sustain that record in much more difficult times, when the pace of innovation is measured not in centuries but in seconds, and competing financial centres are piling on the pressure.

So how is London making out? The short answer is not badly, but could always do better.

At least the authorities are taking the lead. One of the most startling innovations currently under way in the City is the shake-up of the regulatory regime. Soon after being elected in 1997, the Labour government scrapped the mish-mash of bodies which had been regulating the City - sort of - and set up the integrated Financial Services Authority (FSA).

The FSA took four years to get going. But it has been worth waiting for because it streamlines the whole regulatory system, and provides a one-stop shop for City firms which previously might have been regulated by half a dozen different bodies.

This clearly has an appeal both for UK banks and for foreign banks who are setting up in London in growing numbers. For the US banks, who now dominate the London scene, the single regulator marks a refreshing change from the cat's cradle of regulators they have to deal with back home. Many US banks cite the UK regulatory climate as an important reason why they locate in the City.

The FSA is not without its critics: by definition it is large and powerful because it regulates everybody, and it can get miscreants fined or sent to jail. That scares people, and makes them wonder whether London might lose the flexible regulatory touch which has always been one of its strengths. It is too early to tell. But it is significant that the FSA is bound by statute to encourage competition and innovation in the City, which is good news. The FSA's integrated structure also provides an innovative model which other countries are planning to follow - Germany and Ireland, for example.

A very powerful test of London's innovation record has been provided by the introduction of the euro. With the UK outside the single currency, the City is under even greater pressure to display its strengths or risk losing its position as Europe's leading financial centre.

The record so far has been very encouraging. London's skills in trading and underwriting have ensured that the City has not only held its position, but has actually transacted more international business in euros than either Frankfurt or Paris. The bulk of foreign exchange trading in euros takes place in London; more than half the big capital issues denominated in euros have been underwritten in London; and many of the large takeovers and mergers in euroland have been masterminded by London-based corporate finance departments.

Interestingly, London is second only to Frankfurt in the volume of euros it sends through the international payments system, ahead of France and Italy, showing that it is well in there when it comes to euro business. Over the three years that the euro has been in existence, more than 150 European banks have registered to set up in London and none has left - suggesting that the movement is in London's direction and not, as many people feared, the other way.

Much of this success can be traced to the fact that the creative skills in European finance are concentrated in London: if you want to put together a big deal, even one in euros, you head for the City. As a result, London has emerged as the leading European centre for new issues in euro-denominated bonds, for funds specialising in emerging markets, and for Europe's fast-growing hedge fund industry. However, this position cannot be taken for granted. London's record is far from perfect, and the growing strength of euroland's own financial centres poses an increasing threat.

One area where London has been conspicuously slow to innovate is the transition to electronic trading. The failure of the London International Financial Futures Exchange (LIFFE) to abandon old-fashioned floor trading and go electronic led to a serious loss of business to Frankfurt. The London Stock Exchange has also been reviewing its options in the light of an ever-changing scene.

LIFFE ended up being taken over by Euronext, the alliance of French, Belgian and Dutch exchanges - but in a deal that ensures that LIFFE becomes the centre for Euronext's considerable derivatives business. LIFFE itself has also become increasingly innovative. One of its most recent products - futures on single stocks - was launched ahead of the Americans, the traditional innovators in this area, and could transform the nature of equity trading.

But it is not all bad news on the electronic front. Of the 50 or so new electronic exchanges that have been created over the last three years, more than a third chose to locate themselves in London, even though they could, literally, have gone virtually anywhere. This is important because they represent a potentially huge future business. The Swiss have even relocated their entire blue-chip stock exchange to London to be closer to the action.

A new growth area is the market for environmental goods. The City was first to set up an exchange for recycled paper, and is now working on markets for 'green' electricity and carbon emission permits.

Nor should one omit the fact that the City is the only financial centre in Europe which has a think tank specifically devoted to the cause of financial innovation, the Centre for the Study of Financial Innovation, which is sponsored by some 60 institutions to research new financial ideas.

The problem with being at the forefront of innovation, however, is that you also take the risk of failure. Many of London's innovations vanish without trace: some of those fancy virtual exchanges are in trouble; and new entrants to the banking business have come and gone.

The important thing, however, is to have an environment that is conducive to innovation. That means sympathetic regulation, a community that attracts the best talents, and plenty of raw material to work on. London is still strong in all these areas, and is increasingly aware of the importance of remaining so.