City leaders have warned that the London Stock Exchange (LSE) risks losing its dominant position in the face of growing global competition.
That was then - Big Bang brought about an end to 'open cry' trading
Tax cuts and better transport links are essential if London is to maintain its lead over rivals, officials said.
The message comes as the City of London celebrates 20 years since the Big Bang, when sweeping changes were first introduced to the way the LSE is run.
London has become a major player in financial services since deregulation.
The benchmark FTSE 100 index of leading shares has risen by 288% since the Big Bang reforms were introduced on 27 October, 1986, according to research by Clerical Medical.
The Lord Mayor of the City of London, Alderman David Brewer, said competition from rival exchanges across the world was tough, and would "get tougher".
"The City needs the support of all parties if it is to maintain its undoubted success," he said.
Michael Snyder, chair of the City of London's policy and resources committee, added that politicians from all parties should not to be "complacent" about the City's strong position.
"Big Bang marked the start of a period of great success for the UK-based financial services industry," he said.
"Reducing the tax and bureaucratic burden, and building Crossrail, are investments in prosperity which will bring strong returns and City success."
Their comments follow a similar warning from former Chancellor of the Exchequer Nigel Lawson, who was part of the Conservative government which pushed through the market reforms in the 1980s.
The Big Bang radically changed the way the LSE operated, doing away with much of what was seen by critics as a cosy gentlemen's club and internationalising London's financial markets.
Foreign groups were permitted to buy British stock market firms, while the role of brokers and the way in which deals were carried out were overhauled.
Deregulation also led to the end of "open outcry" trading on the floor of the stock exchange, as computer screens and telephones replaced traditional face-to-face dealing.
The widespread changes resulted in an explosion of interest from international investors in London, and currently more than 300 overseas firms are listed on the LSE.
Annual turnover in UK equities has rocketed from £161bn in 1986 to £2.5 trillion in 2005.
But deregulation also led to sweeping changes elsewhere in the fabric of the City of London, as traditional barbers' shops and outfitters were replaced by sandwich bars and gyms.
"Before Big Bang it was de rigeur to have a pint and a pie," said Richard Wyatt, chairman of Panmure Capital, who began his career as a stockbroker in 1980.
"Now it's more common to have takeaway sushi and a bottle of mineral water - both of which were unheard of 20 years ago."