The House gave final congressional approval yesterday to legislation that would sharply restrict textile, shoe and copper imports, and sent it to the White House, where it faces an almost certain veto.

The House passed the bill, which had become the vehicle for a bipartisan attack on record trade deficits, by a vote of 255 to 161, which was 16 votes short of the two-thirds majority needed to override a veto. The Senate passed the bill last month by a margin that also fell short of the votes needed to override a presidential veto.

Support for the bill, which was cosponsored by about two-thirds of the House and more than half the Senate, eroded in the two months since the House approved a version limited to textile imports by a margin of 262 to 159.

The vote indicated that President Reagan's new trade policy, adopted this fall to dampen strong protectionist fervor in Congress, was having an effect on Capitol Hill.

Coincidentally, U.S. Trade Representative Clayton Yeutter last night announced the first results from investigations ordered by the president Sept. 7 into unfair trade practices aggressive approach. Yeutter said the European Community has agreed to reduce its subsidies on canned fruits to give American producers a better chance.

But he said the administration is considering retaliatory action against the Japanese, who have refused to lift import restrictions on leather and leather footwear. A panel of the General Agreement on Tariffs and Trade, which regulates world trade, had found that the restrictions violate Japan's international trade obligations.

Japan, whose trade surplus with the United States is expected to total $50 billion this year, is likely to face another slap on trade from the Reagan administration. Industry sources said the Commerce Department has found that Japanese companies dumped one type of semiconductors in the United States at prices as much as 95 percent below the cost of producing them. The Commerce Department informed U.S. and Japanese companies of the findings yesterday and will make them public later this week. The finding is one step in a process that could lead to penalty duties.

The bill sent to President Reagan yesterday would roll back imports of textiles and clothing from the three leading suppliers -- Taiwan, Korea and Hong Kong -- by as much as 30 percent and permanently limit the growth of shipments from nine other major suppliers -- all Asian nations with the exception of Brazil -- to 1 percent a year.

The bill has been attacked in Congress as discriminatory because it exempts Canada and Western Europe while focusing on imports from Third World nations. Mexico and the Caribbean, however, get special status in the bill.

Shoe imports would be limited for eight years to 60 percent of the U.S. market, and luggage imports would be restricted. The bill also directs the president to negotiate agreements within nine months limiting copper imports in the same way he dealt with steel.

Supporters said the legislation is needed as a result of what Rep. James T. Broyhill (R-N.C.) said was the loss of 356,000 jobs in the textile, shoe and copper industries.

But the opponents called the textile manufacturers the most protected in the country and said the bill would increase prices; put billions of dollars of imports, especially farm products, at risk of retailiation, and violate trade agreements.

House Speaker Thomas P. (Tip) O'Neill called on the president to sign the bill, but its prime sponsor, Rep. Ed Jenkins (D-Ga.) acknowledged that a veto is more likely and called an override "a long shot."

The House decided to adopt the Senate version of the bill, which was less stringent on textile imports but added limits for shoes and copper, to avoid the need for a conference on the measure.

Rep. Morris K. Udall (D-Ariz.) voted for the bill yesterday after opposing the measure when it originally came before the House without copper included. But Rep. Howard C. Nielson (R-Utah) said he was unable to support the bill because he opposes the textile and shoe provisions.