Washington public school officials are cutting back their adult education programs during July and August because of budgetary problems, thereby interrupting classes for many of the 21,000 audlts currently enrolled in the citys basic education courses.

Officials said some of the adult students with upcoming time off from jobs are glad they will not miss classes during their vacations. But many other students are unhappy that they will have to retrace forgotten material in September, when classes are to resume.

Bruce W. Harvey, 20, of 1809 Merlin Ave. NE., dropped out of high school several years ago, but began attending evening classes at the Franklin School Adult Education Demonstration Center when he realized he could not get the computer job he wanted.

Harvey had planned to get his high school equivalency by the end of August - "that's the piece of paper: without that I can't go anywhere" - but now fears that he will forget what he has learned and have to begin all over when evening classes resume in September.

"By this going down, closing in August," said Harvey," my chances of getting a job go down the drain."

For many, the adult education classes are the route to a high school or a job promotion. For others, the centers teach skills like shorthand and typing that will bring a longsought new job or move up the ladder.

And for many part time teachers, the classes for adults provide an important source of summer income. The part-time teachers whose classes have been canceled are "probably the most disgruntled" about the cutbacks, said John R. Rosser Jr., assistant to the assistant superintendent for adult education in the D.C. public schools.

Significant reductions are planned for several of the city's major centers for adult basic education, Rosser said. These include the Franklin School center: Project CALL (Community Adult Learning Laboratory) at the Armstrong Adult Education Center; and the PEILA (Program of English Instruction for Latin Americans) Project.

In addition, Rosser said, funding of part-time teachers at seven adult education centers in the city will end on June 30. These centers direct their efforts toward the elderly, ex-drug addicts, and employees in several D. C. institutions, and are expected to continue to run on the funds of the employers.

Among officials in the adult education program, reaction to the summer cutbacks is mixed. Mary G. Turner, the city's assistant superintendent for adult education, accepts the moves as a necessary evil. She predicts that there will not be any "great impact," with some students returning to school with more test and others recovering after "several sections of strong review."

Reginald H. Lee, an evening counselor at the Franklin center, is more pessimistic. "Some work hard to get here, and if you cut them loose, they may never come back."