Share prices on the stock markets of London, Tokyo, Zurich and much of the industrialized world plummeted today amid gloomy world economic predictions and the continued pressure of high U.S. interest rates.

Prices on the London Stock Exchange, after plunging nearly 30 points by noon -- the equivalent of a 54-point drop in the U.S. Dow Jones index -- closed 17.2 points down, the latest of several near-record drops it has suffered in the last two weeks.

The Tokyo stock market suffered one of its worst days ever, and prices in Zurich recorded their biggest loss in six years. The Duesseldorf stock exchange had its biggest drop this year and prices also plunged in Hong Kong, Sydney, Toronto and Paris.

The major exception to the world-wide stock market drop was the United States, where Wall Street rallied with an 18.55-point rise in the Dow Jones index. The Tokyo market rebounded sharply in early trading Tuesday, however, following the Wall Street rally, Washington Post correspondent Tracy Dahlby reported.

The dramatic drop followed several days of sliding prices in major stock exchanges. Most market analysts have attributed the worldwide slump to fears about the size of the U.S. budget deficit. If the Reagan administration is unsuccessful in meeting its stated budget-cutting goals, many investors abroad fear, extensive U.S. Treasury borrowings could keep interest rates high and lead the world to an economic depression.

Some analysts also said the stock slide could have been given momentum by pessimistic predictions late last week by U.S. stock analyst Joseph Granville, who warned of huge drops on the London, Wall Street and other stock exchanges.

While the losses mean severe economic consequences in most of the world exchanges, they are also expected to have serious political repercussions in Britain.

The drop continued a steep two-week slide being called "the black fortnight" here that has created a crisis atmosphere in financial circles and added considerably to the economic and political problems of Prime Minister Margaret Thatcher. The Financial Times index of 30 leading stocks has now plummeted 96 points in 11 trading days, a drop of 17 percent that has wiped an estimated $30 billion off the paper value of British industry.

Market analysts blame the loss of investor confidence here on growing pessimism about the future of Britain's battered economy and Thatcher's monetarist policies after a period of optimism earlier this year that the country might be starting to pull out of its worst recession in a half-century.

The fall here began Sept. 14 when the government authorized the Bank of England to raise the effective minimum interest rate on bank borrowing from 12 to 14 percent to protect the exchange value of the pound. Partly because of the disparity between the British rate and the 20 percent prime rate in the United States, which has drawn money away from Britain, the pound's dollar value has shrunk from $2.47 earlier this year to $1.78 today.

Analysts said the increase in British interest rates was a big blow to confidence in Thatcher's economic strategy, despite her Cabinet reorganization that same day designed to signal her determination not to change course.

There has been persistent speculation in the financial community here that interest rates may be raised again to approach the record 17 percent reached near the beginning of the Thatcher government before reductions were made to try to help British industry recover from the recession.

"There are fears that interest rates will go up again during the next week because the pound is falling again," said Paul Neild, chief economist of Phillips and Drew stockbrokers, who have long been critical of Thatcher's policies. "There has been a loss of confidence and credibility in the government's overall strategy and a question mark over prospects for recovery from the recession. There is now a grave risk of a renewal of the recession."

London Stock Exchange Chairman Nicholas Goodison, who has defended "the general thrust of government policy" as the only way to restructure the British economy, said today that "confidence will be recovered only if the government's economic policy works, if inflation is seen to be coming down and government spending is being cut."

He indicated that Britain also needed help from the Reagan administration. "The U.S. is not balancing its own budget and is keeping interest rates high," Goodison said.

Britain has had nothing but bad economic news recently. Industrial output has continued to fall, and unemployment is still rising. With the unemployment rate now over 12 percent, the highest among major industrialized countries, nearly 3 million Britons are jobless, more than during the depths of the 1930s depression.

Britain's inflation rate, which had decreased steadily for a year to provide the only statistical sign of success for Thatcher's policies, has turned upward again, increasing last month from 10.9 to 11.5 percent. The growth of the money supply, a crucial indicator in Thatcher's strategy, also has continued to exceed government targets.

Meanwhile, total government spending, rather than being reduced as Thatcher intended, is estimated to increase greatly during the next fiscal year. This would increase the budget deficit and government borrowing, which could fuel inflation and force interest rates up further.

Like Reagan, Thatcher must make more spending cuts this fall. Although her government has already significantly reduced expenditures for housing, education and other public services, deeper cuts in social programs have been thwarted by resistant members of her Cabinet. She fired some of them in her recent Cabinet reorganization and moved others to put less reluctant budget-cutters in charge of most big-spending departments.

Thatcher will still find it difficult to make more cuts. Much of the increase in government spending has been in benefits for the many more unemployed. The recession has increased the money needs of nationalized industries, although they have laid off tens of thousands of workers.

Correspondent Dahlby added:

The crash in Tokyo sent shock waves through the city's financial district Monday as the 225-stock Dow Jones average fell 302.84 yen, its sharpest one-day decline, in value terms. But by midmorning Tuesday it gained 152.34 yen, recovering slightly more than half of Monday's loss.

Previous plunges here have been much greater in percentage terms, and Monday's drop appears to have no serious political implications. If anything, economic crises here tend to bolster the popularity of Japan's Liberal Democrats because after 26 years in power they form the only political party with tested economic expertise.

A major factor in today's drop may have been the recent rush of Japanese companies into the market with public stock offerings in a bid to increase financial reserves.