While long-simmering trade disputes still remain, the relationship between Japan and the United States has improved markedly in the past year.

One symbol of that improvement was Friday's meeting in London between President Reagan and Japanese Prime Minister Noboru Takeshita.Takeshita, who was in London as part of his second trip to Europe since taking office last November, was being briefed personally by Reagan on his talks with Soviet leader Mikhail S. Gorbachev.

Before leaving Tokyo, Takeshita ruled out the possibility that contentious trade issues would come up during the discussion. But on Thursday, Reagan administration officials went out of their way to praise Japan for the progress the country has made in opening up its markets and boosting domestic demand.

For more than two years, the administration has been pressuring the Japanese to adopt policies that will stimulate domestic demand instead of relying on export-led growth.

Domestic demand has accelerated in Japan this year, helping to push the nation's jobless rate down to 2.6 percent in April.

Beryl Sprinkel, the president's chief economic adviser, said Thursday that Japan had done a remarkable job of modifying its economic policies in the past year.

"I can't see how you could be unhappy with the very sharp acceleration in domestic demand. I think everyone has been very pleasantly surprised at what has happened over there in the past year on that front," he said in an interview with reporters.

U.S. and Japanese officials spent three days in Washington this week locked in disagreement on one of those issues, a prolonged dispute between the two countries over opening Japanese markets to more imports of American beef and oranges.

The discussions between Assistant U.S. Trade Representative Michael Smith and Japanese Deputy Agriculture Minister Hidero Maki ended Thursday with no agreement in sight. The Japanese are hoping to reach a settlement of the dispute before the Toronto economic summit begins on June 19, but the American side is less certain the differences can be bridged by that time.

The United States has been demanding total removal of the beef and citrus import quotas that it had accepted in a 1984 agreement that expired in March.

Part of the reason for the easing of tensions between the two nations has been favorable news on the American trade deficit. It fell to a three-year low of $9.7 billion in March, bolstering the president's hand in his current fight with Congress over the omnibus trade bill.

Reagan's veto of the measure is expected to be upheld by the Senate, an event that would be viewed favorably by the Japanese, who felt singled out by the measure.