The Exchange also announced yesterday that it wants Liffe, the futures exchange, to close 20 minutes later, at 4.30pm, to alleviate trading difficulties at the end of the day.
There are to be fundamental changes to the way closing prices are calculated, which the Exchange believes will iron out "rogue", or unrepresentative, closing prices. Rogue closing prices is perhaps the most prominent of the problems that have dogged Sets, the new electronic trading system, since its launch in October.
Sets, although widely regarded as a technical success, has been criticised for producing unreliable prices at the beginning of the day. In addition, only around a third of all trades are currently executed over Sets, with many larger institutions sticking with the old "quote driven" system.
The moves are part of the Exchange's response to its month-long consultation with members over the performance of Sets.
Other proposals include scrapping the minimum order size, which will allow very small holdings of shares to be traded over the new electronic system, as well as raising the maximum size.
The Exchange is to reduce the pre-market period - the placing of buy and sell orders before the market officially opens - from half an hour to 10 minutes. It is considering introducing a central counterparty, a system whereby either the Exchange or another official body guarantees all trade. The Exchange is to consult further on the issue, and has said a central counterparty will not be introduced until after 2000.
The Exchange said it would not move all smaller FTSE 250 stocks onto the new system "at present".
The later opening hours will apply from 20 July, and the new method of calculating closing prices will begin at the end of the year, unless there are marked improvements "in the consistency and predictability" of closing prices.
The Exchange intends to calculate closing prices by taking an weighted average of trading prices over the last 15 minutes of the day. At present, the closing price of a stock is simply the price of at which the last trade of the day is executed.
As far as Liffe's new closing hours are concerned, Martin Wheatley, head of markets development at the Exchange, and the man who has spear-headed the introduction of Sets, said: "Liffe were very positive [about closing at the later time of 4.30] but they need to consult their members."
The Exchange said yesterday that Mr Wheatley would be proposed as a new executive board director. It added that Richard Kilsby, director of market services, resigned from the board at the end of May.
According to the Exchange, feedback from the market had confirmed that "the new trading structure is viewed by users as being sound and technically robust". But the Exchange admitted: "There was a general desire to see more liquidity in the system and more consistency of price formation".
Trading houses broadly welcomed the Exchange's proposals, although several thought they did not go far enough. Some traders expressed scepticism about the effectiveness of the later opening hours.
The Exchange also announced its results yesterday for the year ended March 1998. It returned pounds 16.6m to members, compared with pounds 10m last year, at operating costs fell by 21 per cent.
Simon Robertson, currently a managing director at Goldman Sachs, is to join the board as a non-executive director. Donald Brydon, Robert Metzler, Mark Radcliffe and Bernard Solomons are to retire as non-executives at the annual general meeting on 9 July.