A House subcommittee unanimously approved legislation yesterday to make the Social Security Administration an independent agency starting in one year and to remove its old-age and disability trust fund operations from the federal budget in fiscal 1987.

In a similar move, the Senate, on a 79-to-20 vote, instructed its Budget and Finance committees to draft new rules and legislation by early November to assure that Social Security cuts can no longer be used to reduce federal budget deficits.

The proposal, sponsored by Sen. John Heinz (R-Pa.) and others, had the same aim as the House provision removing Social Security from the budget -- to thwart cuts that are based not on program needs but simply on a desire to make the federal deficit look smaller.

Meanwhile, the Senate Finance Committee deadlocked for a second day over a proposal by Senate Majority Leader Robert J. Dole (R-Kan.) to tack the tobacco price-support bill sponsored by Sen. Jesse Helms (R-N.C.) onto the committee's $38 billion, three-year deficit reduction package in order to help smooth passage of both measures through Congress. A final vote is expected today.

In the Finance Committee, Democrats David L. Boren (Okla.) and Max Baucus (Mont.) protested that although the Helms proposal would help tobacco farmers it would do nothing for wheat, corn, cotton and rice farmers who are also facing hard times.

On the House Social Security bill, Health and Human Services Secretary Margaret M. Heckler said in a letter that the administration strongly opposes taking the Social Security Administration out of HHS and making it an independent agency because it would "disrupt" Medicare, which would remain in HHS and in the unified budget.

The Social Security bill, firmly supported by organizations of the aged, aims to insulate the program from politics and from benefit cuts.

Under existing law, the two trust funds are scheduled to be removed from the unified budget in 1993; the bill would move this forward to 1987.

One immediate fiscal impact of the bill, according to the Congressional Budget Office, would be to make the federal deficit larger. At present, and for the next generation, the old-age and disability funds are running an annual surplus that helps offset the deficit.

If the surplus can no longer be counted, the budget deficit will grow an extra $10.5 billion in fiscal 1987, $36 billion in fiscal 1988, $49.6 billion in 1989 and $67.3 billion in 1990, and nearly $90 billion by the mid-1990s.

Under the Ways and Means subcommittee bill, the Social Security Administration would become a separate agency with jurisdiction over the old-age and disability programs and Supplemental Security Income (federal welfare for the aged, blind and disabled). All other programs would remain in HHS.

The new agency, which would select its own commissioner, would be operated by a bipartisan three-member board appointed by the president (subject to Senate confirmation) for six-year terms. The board would run its own shop administratively but would submit its budget and legislative proposals to the White House, according to the subcommittee.