Such thoughts, which have been floating around the City since Big Bang annihilated eyeball to eyeball floor trading 10 years ago, have been given new impetus by Brian Winterflood, the largest market-maker in small company shares.
In an interview in the latest edition of Smaller Companies Review he warns that if he finds he cannot compete under the order-driven trading system the Stock Exchange is introducing "we might declare UDI and set up our own stock exchange. That is not a bluff but it is something I would not like to have to do".
Any break-away might not be confined to the smaller stock market players. It is known that some of the large investment houses, unhappy with what they see as lack of direction from the Stock Exchange Tower, have talked about splitting from the traditional Stock Exchange share market and launching their own versions.
Mr Winterflood's SCR comments coincided with new worries that the world could face another share melt-down. On Friday fears of a crash erupted with frightening force.
He warned that in an order-driven system trading in the shares of smaller companies could be impossible in a bear market.
Only the top 350 companies enjoy sufficient trading volume to justify order-driven, as opposed to the present price-driven, trading, he believes.
In a bear market there would, he warns, be only sellers in the small company sector.
"It would then become very difficult for fund managers to get a value on their portfolios. Effectively the shares would go unquoted while the bear market raged."
It is, of course, often difficult to trade in shares of smaller companies, even in a bull market. With trading infrequent there is also a natural tendency for market-makers to shelter behind wide spreads.
So the middle market price is often far removed from the dealing level.
Mr Winterflood, head of Winterflood Securities which deals in the shares of nearly 1,500 companies, thinks London's stock market should split three ways.
The top level would, in effect, be a wholesale market traded internationally by large financial institutions. There would be a different set of regulations for the second level market which would embrace the full list of quoted shares with rules to allow price-driven trading in the smaller and medium sized companies. The third market already exists in the shape of AIM.
The wholesale market would soak up all the big business: "We think it foolish to go on pretending that retail holders of stocks and shares can get the same price as the wholesalers. In no other market in the world do we get the guarantee that you get the same price and that everyone is treated the same."
One market-maker has already decided to go it alone. John Jenkins stepped in when the Stock Exchange, surprisingly, decided to do away with the old matched bargain 4.2 market.
He launched Ofex, which now features approaching 150 shares, ranging from old 4.2 stocks like Weetabix to intriguing start-up ventures such as Motion Media. Tradepoint, an order-driven system, has also emerged as, at the moment, a flea-bite rival to the main market.
Order-driven trading, embracing the 100 Footsie shares, is due to start on 20 October next year. It is, however, the Stock Exchange's intention for all shares to be subject to the order-driven system although no time frame has yet been produced.
It has to be hoped that the needs of small investors will be given priority as the new-style trading is thrashed out. Many feel the Government and the Stock Exchange authorities have failed to look after the interests of the small shareholder, caving in to the demands of the big investment houses and fund managers.
Crest, the computerised share settlement system which has suffered such a painful birth, is the latest influence which seems to disadvantage the small man.
This week's results get little support from the big battalions. Biggest reporting is Greenalls, the former brewer which enjoyed a brief membership of Footsie.
Now a hotel, pub and wholesaling operation Greenalls had the sense to give up brewing as the impact of the Government's controversial Beer Orders became apparent. It has, therefore, been able to extend its pub estate without worrying about the retail ceiling formula Whitehall imposed on the big brewers.
On Friday the company at last managed to check out of US hotels. It has sought for years to unload its modest transatlantic chain which, it felt, did not fit in with its operations. The six properties were sold for pounds 14m. As NatWest Securities observes, the disposal represents "a long overdue exit from a business which has rarely been in profit over the past 10 years".
NatWest sees profits emerging 45 per cent higher at pounds 145.5m with the dividend up, perhaps, 8 per cent to 15.3p.
Compass, the expansion hungry contract caterer, could top pounds 115m (pounds 73.2m last time). With around 75 per cent of its profits coming from overseas the recent strength of sterling could be creating a few problems.
Yorkshire Electricity could be called the one that got away - at least for the time being. To many old-fashioned punters it must seem incredible that the group is still independent and able and ready to produce its own profit figures.
At one time it experienced a veritable crescendo of take-over speculation; yet the long-signalled bid failed to appear and indeed Yorkshire says it never received a hint of a solitary approach. Its first-half profits will be sharply down - from pounds 110.6m to nearer pounds 86m.
But the market will be more interested in any moves to return cash to shareholders. A share buy-back - or special dividend - must be likely.