President Carter's hospital cost control bill, which he considers a critical element in his fight against inflation, yesterday cleared its first congressional hurdle.

The bill, which would trigger mandatory controls in 1980 if a voluntary effort by hospitals to hold down costs fails this year, was approved 6-to-3 by the House Ways and Means health subcommittee.

The bill now goes to the full committee, where the chief lobbyist for the Federation of American Hospitals, Michael D. Bromberg, predicted a "very close" vote.

Health subcommittee Chairman Charles Rangel (D-N.Y.) said cost containment might come up in the full committee as early as next week, but could be delayed.

Neverthless, the committee appears to be the best opportunity the administration has for moving the bill to the House floor.

The bill is moving more slowly in two Senate committees which have jurisdiction, Human Resources and Finance, and it faces tough opposition in a second House committee, Interstate and Foreign Commerce.

The House Democratic leadership has set a late July deadline for bringing the bill to the floor and Rangel said yesterday he expects the leadership to bring up the Ways and Means version even if the Commerce Committee has not acted or does not pass it.

Even if the Commerce Committee does not report a bill, House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said yesterday, "I will find a means and a method to get the bill to the floor."

The administration estimates the bill would save $3.7 billion in fiscal year 1980. In a breakdown of that figure the administration said it would save $1.4 billion in the federal budget, over $420 million in state and local budgets and almost $1.9 billion in private health insurance and payments by individuals.

A voluntary effort begun in 1978 by the hospital industry will cut the inflation rate to 11.6 percent this year, they hope. Industry officials claim it is impossible to meet the 9.7 percent goal in the administration bill. That figure could change, however, depending on the inflation rate.

Hospital officials strongly oppose government controls. Last year they successfully held off cost containment legislation, but admit that new emphasis on austerity and inflation will make it tougher to defeat the bill.

If hospitals meet the inflation figure set by the secretary of health, education and welfare, no mandatory controls would go in effect. Controls would stay off for each year that the hospitals meet the figure. And each year the secretary of health, education and welfare would compute the inflation rate limit, taking into account a number of factors.

If mandatory controls were triggered, some 57 percent of all hospitals would escape them. There are exemptions for federal hospitals, small non-urban hospitals, institutions less than 3 years old, hospitals in state where mandatory or voluntary programs are successful and health maintenance organization hospitals would be exempt.

The subcommittee yesterday adopted one important change that would strengthen a provision that forbids a hospital from meeting the limit by changing admission practices to keep out charity cases or patients with costly illnesses. The new language would prohibit changing admission practices to include sending charity patients or emergency room patients to other hospitals.

Otherwise, the subcommittee largely added to the exemptions for certain hospitals. Rep. Harold Ford (D-Tenn.) exempted children's hospitals which draw patients from a wide area and children's hospitals doing research. Shriner's hospitals for children were also exempted.

Rep. Charles Vanik (D-Ohio) exempted clinics which specialize in treating cancer or other specific diseases.

Alaska and Hawaii which have higher rates of inflation were allowed a higher rate of increase.