If Paul Revere were alive and scouting for the British, he would be riding through the streets of London's financial district crying, "The Yankees are coming, the Yankees are coming."

Many banks and investment banking firms in this country are buying British brokerage firms, while others are increasing the size of their London staffs in anticipation of "Big Bang Day." Sometime next year, on a day dubbed "Big Bang" because of the explosion that will shake the financial markets, the London Stock Exchange will be deregulated.

The changes scheduled to take place before the end of 1986 are sweeping. Not only will comfortable regulations such as fixed brokerage commissions on stock trades be eliminated, but the London Stock Exchange will consider granting membership to foreign securities firms for the first time. Those foreigners include a group of Wall Street firms eager to expand their British trading and brokerage operations, because they no longer will have to rely on British firms to execute routine trades on their behalf.

Securities industry experts believe a move to admit foreigners into the London exchange reflects a global trend toward financial deregulation. U.S. industry leaders hope the trend will lead ultimately to the linking of the New York, London and Tokyo stock exchanges, enabling Wall Street firms to freely trade all kinds of financial instruments for themselves and their clients 24 hours a day.

Officials at the Securities and Exchange Commission said last week that problems such as illegal insider trading on U.S. markets could get worse next year when deregulation makes it easier for investors to trade U.S. stocks on the London exchange.

However, the SEC has no specific program to combat potential illegal trading on the London exchange. The regulators indicated that it is difficult for them to act on the issue without the consent and cooperation of British officials.

They also admitted that neither they nor the officials of the London Stock Exchange are sure what current problems may be exacerbated by the changes or what new problems may arise.

In addition to deregulating commissions and permitting foreigners to become members of the exchange, the London Stock Exchange also plans to alter radically the way trades are handled. The British stock-trading system now features "jobbers" as wholesalers and brokers as retailers, each earning a commission on trades. It will be replaced by an electronic-market system similar to the National Association of Securities Dealers over-the-counter market.

In the new electronic system, with the role of jobbers as market-makers eliminated, it is not clear whether trading will continue to take place on the floor of the exchange or whether it will move upstairs, where traders will execute transactions while watching screens filled with information about the latest price and volume of trades.

What does appear certain, experts say, is that some British firms will not survive in this deregulated environment, after years of being insulated from foreign competition. And the big U.S. investment banking firms appear ready and anxious to take advantage of the opportunities created on Big Bang day.

The well-capitalized British brokerage houses -- including those that have allied themselves with well-capitalized partners -- are excited about the changes because they will be permitted to expand their operations into new areas. For example, British brokerage firms will be allowed to underwrite securities for the first time.

Foreign enthusiasm for dollar-denominated securities in 1984 has only added to the drama, as many American corporations have taken advantage of the foreigners' appetite for these securities by raising more capital abroad in the Eurobond market than in the U.S. markets.

And the international merger and acquisition advisory business is yet another arena the Americans are trying to enter through London. With lucrative merger advisory fees abroad seemingly within their reach, American investment bankers have increased their marketing efforts to encourage their selection as advisers in transactions between two European companies, going beyond their traditional role of representing U.S. companies involved in transactions with foreign corporations.

"What they plan by Big Bang day is to open up the membership of the stock exchange to people like us, introduce negotiated commissions, introduce a totally new dealing system for equities and totally restructure the U.K. government bond market, all of which makes May Day here in the United States look like a Sunday afternoon picnic," said David J. Rochester, director of international strategy and market planning at Merrill Lynch, comparing London's deregulation to the May 1, 1975, abolition of fixed brokerage commissions in the United States.

"The changes will mean we can be as competitive as anybody else in London. Now we have to pay commissions [on trades] and go through London brokers. The changes also mean we can get involved as a primary dealer in British government securities," Rochester said.

Merrill Lynch, which already had a London brokerage operation that marketed U.S. securities, has chosen thus far to expand its staff in anticipation of the changes, instead of acquiring British firms. Rochester said Merrill Lynch employs 850 people in London.

Shearson Lehman Brothers, which has about 200 people in London dealing mostly in U.S. securities and commodities, chose to go the acquisition route, purchasing a 29.9 percent stake -- the legal limit -- in London's L. Messel & Co. By Big Bang day next year, the firm will be allowed to complete the purchase of L. Messel.

Jeffrey B. Lane, vice chairman of Shearson Lehman, said the acquisition gives the firm a London investment banking presence, as well as a local distribution capability for U.K. and U.S. securities.

"As the stock markets move toward a 24-hour trading capability, we want to have the ability to trade for our institutional, retail and corporate clients worldwide," Lane said, reflecting a point of view shared by almost all of his competitors. "Our London strategy is part of our worldwide strategy."

Goldman, Sachs & Co. has decided to build, rather than buy, a greater presence in London. The investment banking firm has tripled its London staff from about 60 to 180 people in the last several years.

"They are shaking up The City [London financial district] and replacing it with an entirely new structure modeled very much on the American market for government securities and the over-the-counter market, while ending fixed commissions and the exclusion of foreigners," said Roy C. Smith, who recently returned to the United States after heading Goldman's London office for the last several years. "It is a horrendous change for the British , because not only does everybody have to run out and merge with everybody else, they have to learn to operate in competition with all the heavy players from other countries. It makes what we did in deregulating the airline industry look tame."

One of the most aggressive acquirers of London financial firms has been Security Pacific Corp. The Los Angeles-based bank has purchased stakes in three London firms. Robert H. Smith, the bank's vice chairman, said Security Pacific wants to establish a London presence in the brokerage, investment research and corporate finance areas. Smith said the acquisition of "the leading equity broker in the U.K.," Hoare Govett Ltd., has enabled Security Pacific to consider expanding the investment services network to Australia.

"Almost everybody starts with the premise that London will be the principal international financial center in this time zone, and everything happening here is a vote of confidence for London in the future," said Archibald Cox Jr., managing director of Morgan Stanley & Co. and head of the firm's London office.

"It is logical to see these mergers and to see what U.K. entities like Warburg put together," Cox said, referring to London's S. G. Warburg & Co., which has taken advantage of the deregulated environment to put sales, trading and underwriting functions under the same roof. Before deregulation, London's financial community was highly fragmented, with different houses performing these investment banking functions.

Otto Schoeppler, chairman of Chase Manhattan Ltd. in London, said the giant bank has entered into agreements to purchase two U.K. firms, one specializing in brokerage and underwriting services and the other specializing in trading gilts, which are British government securities. The Americans entering London frequently mention gilt trading, which will be changed significantly by Big Bang day, as one of the promising opportunities.

"By acquiring two well-established concerns, this gives us a foothold in London more quickly," Schoeppler said. "Also, the business done by these firms can be globalized quickly using Chase's resources and networks around the world. This transcends London. We are dedicated to building a global investment banking capability."

"In New York, the May of 1975 deregulation of brokerage commissions was accompanied by a certain amount of blood, but they didn't have to reorganize their dealing system, too," said a London Stock Exchange official. "We are number three in size after New York and Tokyo . . . But once the electronic stock trading network enables market makers to display prices on screens and trade upstairs, our trading floor may be empty. We just don't know for sure what will happen."