Britain's national steel strike ended after 13 weeks today when union leaders accepted an independent commission of inquiry's recommended pay raise of about 16 percent including productivity bonuses -- only a little more than the British Steel Corporation's last offer and less than Britain's 19 percent inflation rate.

Although the labor dispute did great damage to the already ailing nationalized steel industry, its outcome is a victory for Prime Minister Margaret Thatcher's Conservative government, which had refused to increase its subsidy to British Steel to finance a larger pay settlement.

Thatcher's policy of forcing nationalized industries to cut costs and become competitive to survive showed further results today when one of the two major unions at British Leyland, the giant government-owned automaker, decided to accept without a strike an austerity wage settlement. It provides for pay raises of just 5 to 10 percent, all dependent on improvements in productivity. The plan also will eventually eliminate the jobs of a third of British Leyland's 85,000 employes.

The steel settlement also requires improving productivity, cutting the work force of 130,000 by a third, shutting down a number of huge plants and breaking even financially by the end of next year. The British steel industry lost about $2 million a day before the strike and about double that since.

The strike also cost British Steel about 10 percent of its already shrinking market to foreign competitors and Britain's much smaller and specialized privately owned steel firms. Labor and management morale was left even lower than it had already been because of the industry's deterioration.

During his testimony before the commission of inquiry over the weekend, British Steel Chairman Bob Scholey noted that although the steel strike was Britain's longest postwar national strike, it had little impact on the rest of the country, considering that steel had been heavily stockpiled beforehand.

"If there is one thing out of this strike which we have demonstrated," Scholey said, "it is that the industry we thought was basic to the country was less basic than we thought, and I'm very sad that's happened."

The end of the steel strike also meant that Thatcker has reached the end of a relatively mild winter for labor disputes, which give her at least another year before facing a major confrontation with Britain's unions over her economic austerity and tough labor law policies.

Worse trouble was avoided this winter by pay settlements exceeding the inflation rate for some workers, and by fear of others of a public back-lash against the unions if last winter's politically damaging labor strife was repeated.