While small, some might say insignificant, the competition has sparked consternation. Both the Securities and Investments Board and the Stock Exchange have issued discussion documents on the subject in recent weeks. The established order may be under little immediate threat, but the potential for a long-term upheaval is present.
The London exchange is one of the few in the world to guarantee liquidity - the ability to make a trade at any time - via a quote-driven system. At its heart are the market makers - brokerage houses committed to buying and selling at quoted prices. If no one else wants to buy a falling stock, the market makers will, and vice-versa.
The danger is that this cosy set-up will be undermined by investors, both private and institutional, getting direct computer access to rival exchanges at home and abroad. New order-driven exchanges, which require both an outside buyer and seller, face high start-up costs and have a steep climb to reach the volume levels that will assure participants reasonable liquidity.
But new technology is lowering those hurdles. Computers cost less each year, and off-the-shelf software to supply financial information is filling retailers' shelves. Both CompuServe and the new Microsoft Windows 95 offer on-line US share prices, although the cost up to now has been prohibitive for small investors and purchasing shares still involves calling a broker.
The first tentative step towards Internet share-dealing will be taken this Friday, when Electronic Share Information, a small Cambridge company, and ShareLink, the discount broker, reveal a new on-line service. The launch is expected to showcase a system that will deal through the London exchange. But it could just as easily connect to Tradepoint, a deal-driven market that will begin trading in the UK's top 400 stocks on 21 September. And if Tradepoint, why not Wall Street?
Perhaps even more significant, the Internet could make London stocks available to millions of small investors around the world. This could shift the balance between City institutions and outsiders, though how much is anyone's guess. If it were sizeable, and if it were funnelled through a rival, the exchange could lose its ability to set prices.
The biggest remaining obstacle is settlements. Users of the ShareLink- ESI system will probably have to hold an account with ShareLink, which will go through the usual London exchange channels to transfer funds and titles to the shares. Setting up a separate computerised settlement system is hugely expensive and fraught with danger, as the exchange itself learnt a few years ago when it was forced to abandon Taurus, its paperless system.
There could be other problems. With separate exchanges offering different prices, it would be more expensive for investors to spot the best one. Administrative costs might also be duplicated. But supporters of the new diversity argue that competition usually drives costs down. And if Internet trading does take off, it would be better to have strong UK contenders.