The House Social Security subcommittee aegreed yesterday to shift the date of the annual Social Security cost-of-living increase from July 3 to Oct. 3 to help achieve budget savings sought by Congress and the president.

The change, which would reduce payments by $700 million in fiscal 1982, would be in two stages: instead of getting a single cost-of-living increase on July 3, 1982, beneficiaries would receive half the cost-of-living increase on May 3 and the other half on Oct. 3. This two-payment system would apply only in 1982. After that, increased would be paid only once a year, in October.

The new system, as tentatively approved by the subcommittee, also contains technical changes in base-year calculations that would provide additional savings each year -- $1 billion in fiscal '83, $1.1 billion in fiscal '84 and slightly larger savings each year thereafter because of a time lag between the actual increases in the cost of living and payment of the automatic benefit increase. But these savings may be reduced later if the time lag is eliminated.

For the moment, the subcommittee duced away from changing the actual cost-of-living formula, which would produce much larger savings, because, Rep. Richard A. Gephardt (D-Mo.) said, it is "too much political dynamite." President Reagan opposes a formula change at present.

Other changes voted:

Rounding down monthly payment checks to the nearest dollar, which would produce a saving of about $45 million in fiscal '82, rising to $500 million by 1986.

Placing a cap on gross disability programs (excluding veterans' disability programs) equal to 80 percent of the individual's former earnings.