The Prince George's County Council yesterday approved $5.4 million in public works and housing programs that are funded through federal community development block grants. But the total was 22 percent lower than the council had expected because of federal funding cuts under the Gramm-Rudman- Hollings spending limit law.

The money is mostly targeted for the 22 municipalities in the county where about one-third of the county's people live. Most of the funds are to be spent on streets, gutters, storm drainage and sidewalks.

In the previous 11 years of the block grant program, Prince George's received $68.9 million, of which 46 percent was spent on such public works improvements and 20 percent on housing rehabilitation.

To help fill the gap left by the federal block grant cuts, County Executive Parris Glendenning is scheduled to ask the voters today to improve a large public works bond issue in November.

The vote was 7 to 1 to approve the paperwork required by the U.S. Department of Housing and Urban Development, which provides the money for the block grant program. Council member Sue V. Mills dissented on the grounds that her southern county district will get nothing.

To pare down the block grant program from the earlier budgeted figure of $6.6 million, cuts were made in most areas. In Mount Rainier, for example, $90,000 will be allotted to public works, instead of $110,000 as planned.

But the council added at least one program despite the cuts. The county will spend $80,000 to provide indoor plumbing to low-income families. According to the 1980 census, there are 759 households without indoor plumbing.

Mills said it was unfair that almost all the funds went to municipalities, although unincorporated areas are also eligible for grants. However, the council did set aside $798,000 for street improvements in unincorporated areas, compared to $1 million initially planned.

Voting for the spending were William B. Amonett, JoAnn T. Bell, Frank P. Casula, Anthony Cicoria, James M. Herl, Richard J. Castaldi and Hilda R. Pemberton. Floyd Wilson was not present.