Stock prices around the world bounced back today as dramatically as they fell yesterday, with financial markets from Tokyo to London responding to a turnabout that began on the New York Stock Exchange.

The Tokyo market average rose by a record 320.56 yen after falling 302.84 yesterday. The Financial Times index of 30 leading stocks on the London exchange regained a record-tying 23.7 points after losing 17.2 points yesterday and nearly 96 points in the past two weeks.

Market analysts here said today's recovery represented both a normal adjustment after a prolonged period of falling stock prices and a steadying of jittery investors' nerves by the late rally on the closely watched New York exchange yesterday.

Just as the plummet in prices elsewhere followed a shock wave of pessimism from New York over the weekend, the analysts said, the upsurge moved through the globe's time zones overnight from New York to Tokyo and Sydney and then to Europe.

The New York Stock Exchange also picked up where it left off, albeit at a more modest pace. The Dow Jones Industrial Average was up 5.33 points on the day, closing at 847.89. Details on Page D9.

Tim Brown, an analyst here with Phillips and Drew stockbrokers, said, "A market overdue for technical adjustment basically followed the U.S. lead today. We have been tremendously overdue for a rally."

But he and other analysts said the London exchange, like most other financial markets in Europe and the Far East, remained quite unsettled and still well below midsummer price levels. The big question, analysts said, is still whether the Reagan administration's economic strategy will work against the high U.S. interest rates that have destabilized currency values and stock prices.

Brokers in Tokyo continued to maintain that Monday's sharp decline was primarily the result of Wall Street's poor performance in recent weeks, Washington Post correspondent Tracy Dahlby reported from the Japanese capital. They predicted that Tokyo's fortunes would continue to be closely tied to New York trends but that the underlying strength of Japan's economy should mitigate medium- and long-term share price fluctuations.

In Paris, the Bourse jumped 2 percent and trading in five issues was temporarily suspended because of an influx of buying orders.

In Frankfurt, share prices recovered sharply. The Commerzbank index rose 12.2 points, erasing a similar 12.2-point drop Monday.

In Amsterdam, the ANP-CBS general index rose 3.7 to 82.2 in a broad recovery. Gaining issues outnumbered losers 3-1.

Other gains, after sharp losses Monday, were reported on the Oslo and Sydney stock markets. Bucking the trend were Singapore, Hong Kong and Milan.

While disparaging the prediction of maverick U.S. financial analyst Joseph Granville that the U.S. and European stock markets would virtually collapse this week, many analysts here agreed with Granville's forecast that stock prices still could fall much lower in the months ahead unless the U.S. produces surprisingly good economic news.

"We see little growth in the U.S. over the next 12 months," said chief economist Paul Nield of Phillips and Drew, "so we expect U.S. interest rates to stay high until Christmas at least. Can we hold out until Christmas?"

Speculation continued about whether Prime Minister Margaret Thatcher's government would push interest rates nearer to U.S. levels to protect the exchange value of the pound sterling, which also reversed course today, rising from $1.78 to nearly $1.80. Economists and politicians of all parties here have warned that such a move would deepen Britain's severe recession.

In the past two weeks of plummeting prices, stockbrokers here said, much of the selling was by institutional investors reacting to gloomy economic news and forecasts, plus the falling market itself. Big institutional investors largely stayed out of the market until today, when brokers said they began buying leading stocks at what appeared to be bargain prices.