Change is sweeping through the tiny streets, staid buildings, and trading floors of the City of London, the world's largest financial center. ''The City has triumphed remarkably over the decline of the British economy and of sterling,'' says William Clarke, a former financial correspondent who is now deputy chairman of the Committee on Invisible Exports, a group that deals with British overseas earnings from such noncommodity exports as financial services and consulting.
''The question now is whether in the future London can withstand the growing challenges of other centers, such as New York, Chicago, Zurich, Paris, and Frankfurt.''
The City is built on the oldest spot in London, where the Romans built walls and temples 2,000 years ago. A mere square mile in area, the City of London is a clublike maze of Lombard Street banks (there are more US banks here than in New York), Leadenhall Street shipping offices, Thames-area gold and other commodity markets, Lime Street insurance houses, the Stock Exchange, and the Bank of England. The district is unmatched in its 24-hour-a-day variety, know-how, and flexibility.
But the City's penchant for self-regulation and its often old-fashioned ways have their critics - especially in the wake of alleged fraud at Lloyd's of London and questions about Stock Exchange practices.
The City, says Mr. Clarke, is like a village: You can walk across it in 15 minutes, it thrives on gossip, it readily adopts a ''them'' and ''us'' approach to life, and ''it needs and trusts its village policeman and abhors outside interference.''
Twice in recent days, however, the villagelike atmosphere has been punctured by outside critics while worldwide investors tried to gauge the pace and relevance of London changes in an era of electronic trading and intense competition.
* The Conservative government has struck a deal with the famed Stock Exchange to bring about some reforms in return for avoiding a complex restrictive-practices lawsuit that has already taken four years and a total of (STR)3 million ($4.5 million) to prepare.
The government says it acted to bring the Stock Exchange into line with the European Community and to avoid damaging the exchange's smooth workings.
Critics reply that the government is helping the exchange avoid a court case it could not win, in part to benefit huge pension funds that use the exchange extensively and in part to help the government's ambitious plans to sell off state assets, mainly through the sale of corporate shares.
A leading City financial figure commented in an interview: ''Self-regulation is all very well, but clearly some of the Stock Exchange rules are restrictive.
''In the US you have your Securities and Exchange Commission, your federal and state legislation, and so on. We don't - but we're starting to be stricter now.''
* One of the contenders for leadership of the opposition Labour Party, Roy Hattersley, has just argued there is a need for banks, stockbrokers, commodity brokers, and others to be licensed by the government.
He said the City is interested in quick profits rather than long-term growth. It should be forced to invest in British manufacturing industry. A new Labour government would set up a public body accountable to Parliament to see that pension funds and life insurance companies invest in the public interest.
Mr. Hattersley also attacked the government move to exempt the Stock Exchange from its restrictive-practices lawsuit, claiming the Tory govermment was trying to help its own supporters.
The reaction in the London Stock Exchange was immediate and frosty.
The chairman, Sir Nicholas Goodison, agreed that British industry had found it hard to raise money in the 1970s. But he said that was because industry had been unprofitable, not because money was lacking in the City.
He rejected the charge that City money did not help new industry. He insisted that not only City institutions but also High Street banks throughout the country are willing to consider plans by young companies.
In each of the last two years, Sir Nicholas said, (STR)3 billion ($4.5 billion) had been raised by United Kingdom companies through the London Stock Exchange. An attempt to turn British industry around by creating a national investment bank administered by government bureaucrats would be impractical and unworkable.
The government has extracted changes to open up the Stock Exchange, in return for action to be taken later this year to exempt the exchange from the Restrictive Practices Act.
The exchange will phase out minimum charges on buying and selling shares within three years, a move long wanted by the big pension funds and other institutions. (Wall Street abolished fixed commissions in 1975.) It will allow nonmembers to sit on its ruling council. It will set up an appeals committee to hear complaints from those whose membership has been refused and will permit nonmembers to serve as directors of Stock Exchange companies.
A practice widely commented on abroad will remain, however. It is the system unique to Britain that says that only brokers can deal with the public, and only ''jobbers'' can actually buy and sell shares on the exchange floor.
Critics, including the government's own Office of Fair Trading, which brought the original lawsuit four years ago, claim the London system is restrictive. Members argue the opposite, saying that brokers avoid conflicts of interest between buying and selling shares by going to jobbers, and that jobbers provide healthy competition and impartial trading conditions.
Changes have also come recently in the huge Lloyd's of London insurance market after a series of multimillion-pound cases of reinsurance fraud - members assuming risks on behalf of a syndicate of clients, then reinsuring the safer parts of those risks with companies formed in tax havens abroad by the members themselves.
The Bank of England, which supervises the City in a tight though informal way , has appointed two outsiders to a new governing committee of Lloyd's, which also has a new chief executive.
Meanwhile, the City remains a formidable center for world currency, commodity , insurance, and futures trading as well as banking, accounting, and financial consulting.