Lloyd's of London, the 300-year-old insurance market, weathered a series of frauds in the late 1970s and early 1980s, but now is under serious attack because of continuing problems.

Lloyd's faces a growing clamor among politicians and financial experts in London to end the unique system of self-regulation and special legal exemptions that it has enjoyed for centuries..

The scandals of the late 1970s and early 1980s culminated in the Peter Cameron-Webb (PCW) affair, in which hundreds of investors lost hundreds of millions of dollars.

Directors of the underwriting agency known as the PCW Agency were accused of fraud and of having used investors' money for their own private business and pleasure.

In the aftermath, Lloyd's governing council headed off calls for outside supervision by enacting its own far-reaching reforms, which included strengthening disciplinary procedures and increasing disclosure requirements for its members.

The brokers congratulated themselves on having survived the most serious attack on Lloyd's traditional way of doing business in living memory.

But in the last few weeks, a series of developments have breathed new life into old scandals and even added a few. Peter Miller, the chairman of Lloyd's Council, has been confronted by accusations in Parliament of conflicts of interest.

And there is a growing movement in the British Parliament to replace the 1982 reforms with a new and much more draconian system to police the 300-year-old insurance market.

The most important of these developments are:

*The resignation of Lloyd's chief executive, Ian Hay Davison, on Nov. 11, to take effect next May. Davison was appointed in 1983 by the Bank of England, the British central bank, specifically to clean up the scandals and see the reforms through.

Only a few months ago, he was talking of needing a full five years to complete work. His resignation is a tacit admission that he has lost his struggle to remain a force independent of Lloyd's Council, especially as its chairman.

*The announcement of penalties against six individuals implicated in what Lloyd's calls "dishonest misappropriation of funds" in the PCW affair. Four were suspended and two expelled from Lloyd's membership. One of the expelled, Peter Dixon, was fined one million pounds ($1.48 million), the largest fine in British financial history.

Nevertheless, critics denounced it as a "sick joke" by comparison with the massive sums Dixon and his colleague Cameron-Webb are alleged by Lloyd's Disciplinary Committee to have stolen from investors during more than a decade.

Moreover, there is little prospect that Dixon, who is believed to be in Costa Rica, ever will pay the fine. Cameron-Webb, who allegedly was the brains behind the entire operation, escaped discipline by resigning and moving to Florida, where he sells insurance at Miami's Insurance Exchange of the Americas.

*Earlier last month, British government investigators revealed that they have found evidence of another fraud involving a company called Unimar, also part of the PCW empire.

In monetary terms, Unimar is small potatoes compared with its predecessors. Its significance is that Unimar twice has been cleared by internal Lloyd's investigations, one of them conducted personally by Sir Peter Green when he was chairman.

*A Labor Member of Parliament, Brian Sedgemore, recently has claimed that Green and the present chairman, Miller, are subject to conflicts of interest and should resign their positions. He has accused Green of specific thefts of money from insurance syndicates for whom he acted as agent.

Lloyd's is not a company, but a market, in which 5,000 "working members" sell insurance to customers around the world.

The liabilities are underwritten by the market's 26,000 working and nonworking members. Members must have 100,000 pounds sterling in liquid assets to join. As underwriters, they have unlimited liability -- they can be personally bankrupted if their syndicates end up with too many heavy claims. But in good years -- and Lloyd's has had a lot of those -- they do very well, thanks mainly to the innovative underwriting skills of the working members.

For centuries, Lloyd's has governed itself as a kind of gentlemen's club. It has immunities from much of the laws and regulations that affect other financial institutions.

It is a bastion of class privilege in its most impeccably British form: It is not easy to find a senior member at Lloyd's whose father was not also a member.

But unlike other such institutions, it has not fallen behind the times. On the contrary, Lloyd's skills at leading the world in new kinds of insurance policies and new sorts of risks continue to earn it worldwide admiration.

Next year, Lloyd's expects to earn about eight billion pounds (nearly $12 billion) in premium income -- over half of which would come from the United States.

Policyholders may love Lloyd's, but many investors no longer do. As business grew in the 1970s, Lloyd's needed to attract more investors, known in Lloyd's quaint terminology as "Names."

In the past 15 years, the number tripled. Most of the newer Names had no financial experience whatsoever. They include millionaire farmers, members of the British aristocracy, sports stars and even three members of the Pink Floyd rock group.

In this period of rapid expansion, a few insiders took advantage of the trust on which the entire system was based.

Behind a maze of insurance, reinsurance, brokers' fees and commissions, unsuspecting Names were defrauded out of millions of pounds. Some estimates of the total cost of the PCW affair go as high as 130 million pounds ($192 million).

In 1982, Lloyd's headed off a move to replace self-regulation with outside enforcement. In exchange for being allowed to keep its immunities, Lloyd's had to agree to overhaul and toughen all its rules. It also had to accept an outsider, Davison, to supervise the new system.

In spite of Davison's resignation, Chairman Miller argues that, with new rules on disclosure, monitoring of premium income and excessive broker power and so on, Lloyd's self-regulation is now completely different from the system prior to 1982, and affords excellent protection to the Names.

"We have now a modern and up-to-date system of regulation which is the most sophisticated, detailed and carefully-thought-out in the world," he said.

But many Names regard the recent allegations as evidence that little has changed.

Keith Whitten, 39, a director of an executive-search agency, lost "a six-figure sum" in the PCW affair. He was active in setting up the Association of Lloyd's Members to lobby on behalf of the Names.

"Lloyd's is still run by the insiders for the benefit of the insiders," he said.

"In the PCW affair, only Dixon got a fine, and that will never be collected," Whitten said.

"The others all got penalties, like 12-month's exclusion from the market, for what boils down to straightforward theft."

It is Lloyd's bad luck that all this is hitting the headlines at the same time as two other developments: Prime Minister Margaret Thatcher's new financial services bill, which will beef up regulation of all the other British financial institutions, and, entirely coincidentally, allegations of other financial frauds, notably at Johnson Matthey Bank.

Bryan Gould, Labor Party spokesman on finance, is mounting a campaign to put Lloyd's within the financial services bill, a move that would supplement self-regulation with a powerful government-appointed watchdog, on the pattern of the Securities and Exchange Commission in the United States.

"It's clear that Lloyd's is incapable of regulating itself effectively in the interests of investor protection," Gould said.

"In such a situation, conflicts of interest always arise," he added.

In usual circumstances, Labor easily would be outvoted by the Conservative majority in Parliament.

But at the moment, many Conservatives are deeply worried about the issue -- especially in light of the embarrassing number of alleged perpetrators of fraud who seem to be evading prosecution.

In recent weeks, the British government has been forced to admit that its fraud squad is understaffed, and it has accused foreign governments of impeding complicated fraud investigations in London. The political importance of the fraud issue continues to grow.

When the British government announced the details of the financial services bill, Trade Secretary Leon Brittan defended Lloyd's exclusion from the bill, saying that all the scandals now under the spotlight date from before the 1982 regulatory regime. He was attacked not only by Labor, but by Liberal and Social Democratic members of Parliament as well.

Whether Lloyd's opponents pick up the vital Conservative support they need when the formal Parliamentary debate and committee proceedings begin in January will depend not only on how well Miller is seen to be managing Lloyd's continuing problems, but also on whether government investigators have made any progress on fraud prosecutions elsewhere in the financial world.

At the IEA in Miami, Peter Cameron-Webb is reported to be a "star" underwriter. IEA President Arturo Toro recently defended his presence there, arguing that no criminal act has yet been proved against him. In the United States, a man is innocent until proven guilty, he argued.