Social Security benefits will go up 9.9 percent in July to match increases in the cost of living, Secretary of Health, Education and Welfare Joseph A. Califano Jr. announced yesterday.

The increases in monthly benefits, starting with checks to be received July 3, will go to 35 million people on the Social Security old-age and disability rolls. Mandated by law under an automatic cost-of-living formula, the increase will cost the government $10.2 billion in fiscal 1980. It is the largest single automatic cost of living boost since such increases were written into the law by Congress in 1972.

Califano said about 3.9 million people in the Supplemental Security income program for destitute aged, blind and disabled persons also will receive a 9.9 percent boost starting with checks received June 29.

"These automatic increases help the elderly and the needy of our nation to cope with the terrible effects of inflation," Califano said. "This we must do, for these citizens, many with fixed and often meager incomes, cannot be left alone to fend for themselves against the corrosive impact of inflation."

At present, the maximum Social Security benefit for a worker retiring this year is $503.40, not counting a wife's benefit. With the increase, this will go up to $553.30. The current average benefit for an aged couple, $439 a month, will rise to $482.

Under the SSI welfare program, the maximum benefit for an individual, $189.40 a month, will rise to $208.20 a month with the June 29 increase.

The cost-of-living increases will not mean any increase in Social Security taxes beyond those already scheduled by law, officials said. The present tax rate is 6.13 percent paid on income up to $22,900 a year. In 1980, the rate will remain 6.13 percent, but the maximum taxable wage will rise to $25,900. For 1981, the current law calls for 6.65 percent on a maximum of $29,700.

It is conceivable, however, that if inflation continues at the very high rate of the last year, the tax schedule might have to be changed again in future years.

The automatic cost-of-living increases in Social Security benefits are considered one of the major protections for the aged against loss of purchasing power from inflation. Private pensions normally do not pay automatic increases to match inflation.

The increases for Social Security, voted in 1972, first became payable in 1975 when the increase was 8 percent. In 1976, it was 6.4 percent; in 1977, 5.9 percent, and in 1978, 6.5 percent.

Califano said that based on consumer price index figures made available yesterday, prices were 9.9 percent higher in the first three months of 1979 than in the first three months of 1978. Therefore, the 1972 law required him to raise benefits 9.9 percent.

Monthly Social Security benefits are paid to aged persons who have been employed in jobs subject to the Social Security tax and to younger disabled workers-and to dependents and survivors of aged, disabled or deceased workers.