TO A MOVIEGOER of the right age, it's not news that there is romance in the insurance business carried by Lloyd's of London. I dimly remember learning long, long ago that Tyrone Power founded both it and, I believe, the British Navy, with the help of his boyhood chum, Lord Nelson. Reality is only a little less colorful. The true Mr. Lloyd, Godfrey Hodgson tells us, was a stocking-knitter who opened a London coffee house in 1687. It attracted a dockside clientele of merchants who took to meeting there with underwriters who would insure their vessels and cargoes. Two centuries later, Lloyd's had become the world's most important repository of maritime confidence and information, a renowned and much-publicized institution of the Empire.

Today Lloyd's has come still further from cups and saucers and protecting windjammers against pirates and privateers. Among other things it now insures supertankers against spills, nuclear reactors against meltdowns, art masterpieces against damage and rich businessmen against kidnaping. But the basic transaction remains unchanged. A broker approaches an underwriter in Lloyd's huge London headquarters with a proposal to insure a client against some misfortune. If willing, the underwriter does so for a premium which increases in proportion to the risk.

Nowadays, of course, the broker may be a gigantic firm. The underwriter may sign for a syndicate representing dozens or more of private and corporate fortunes, known by the simple and lovely title of "the Names." Lloyd's itself is simply a self-governing association of underwriters. The premiums, commissions, losses and claims may run into hundreds of millions, and there may be several layers of "reinsurance" and complicated clauses of exceptions and limitations to protect the insurers.

But the business remains an intriguing mixture of gamble and calculation. If Lloyd's guesses the probabilities rightly, overall premium income should exceed payout by a reasonable margin. But unexpected disasters -- a pair of oil spills in a single year, a surprise revolution, an upheaval in some industrial market -- can be disastrous.

The operative word is still ''risk." Each member of a syndicate is responsible, down to his shirt and socks, for making good the insured's losses. But there's another vital word -- "trust." The broker must not fudge the facts about the dangers of his proposition in order to wangle a cheaper premium. And in turn, Lloyd's continued prosperity depends on the absolute confidence of the insured that every claim of loss will unhesitatingly be made good. The great story of its golden age of expansion tells of how, after the 1906 San Francisco earthquake and fire, head man Cuthbert Heath, who had led in getting Lloyd's involved in American real estate coverage, cabled: "Pay all our policy holders in full irrespective of the terms of their policies."

Modern times put a terrible burden on such good faith. The competition is cutthroat, the stakes astronomical and the cast of characters international and decidedly non-clubby. There are new and unexpected perils, like hijackings. There are also special temptations. For example, underwriters can accept some very bad risks and still come out ahead thanks to the returns on invested premiums guaranteed by high interest rates.

MOST OF Hodgson's story deals with how such recent changes rocked the gentlemanly old Lloyd's system and what happened as a result. His chapters are case studies. Item: the flap when it seemed that American insurance companies (which bring in a huge share of Lloyd's business) might take over the establishment. Item: the case of the ingenious rascals who bought and filled a tanker, clandestinely delivered the oil to South Africa in violation of a boycott, then scuttled it and had the brass to claim full restitution for ship and cargo. Item: the Savonita case, a phony claim for a cargo of Fiat automobiles, suposedly damaged by a fire at sea, which later turned up in mint condition to be resold in Italy. Item: the scam by which a Lloyd's underwriter, Tim Sasse, was taken in by brokers who unloaded on him a portfolio of insurance on low-quality, high-risk American real estate, and made extra money by skimming the premiums, which were routed through various dummy organizations.

In the last-named case, the members of the syndicate went to the courts to protest the claims. It was both a breakthrough and a scandal. The stock reaction of Lloyd's top brass had always been to hush up problems and pay off, in order to save reputation.

But the climate of the 1970s and 1980s was different. So neither the London journals nor Parliament proved willing to play the game of letting the Names take a bath, with heavy impact on financial markets, in order that Lloyd's old boys might continue to look all-wise. The frauds were aired, and regulatory legislation -- not for the first time in Lloyd's history -- was proposed and passed, as Lloyd's approached its fourth century.

What Hodgson is presenting, then, is the evolutionary tale of how a business run by 18th-and 19th-century class and club rules has had, willy nilly, to change, and why. And if this is kept in mind (as well as those fundamental rules of the insurance game, which can be masked but never changed), then the formidable detail in which each episode is related (this is no work for skimmers) is no longer a barrier, but an exposition.

Business history is like that. It can be -- as Hodgson obviously realizes -- a superior kind of social and institutional record. Ninety per cent of what appears in the business press ignores this truth, being primarily occupied with who is making the most bucks the fastest and why, and couched in the current jargon of management training. But a good journalist who is unafraid of hard work can trace out the underlying patterns for patient and attentive readers. Such readers will find this a richly rewarding venture.