The public employes department of the AFL-CIO, accusing President Reagan of "misleading" the public by presenting himself as a supporter of better schools, issued detailed figures yesterday showing cuts in federal education spending in each of the nation's 435 congressional districts.

For Washington, Maryland, and Virginia, the study said that since Reagan took office, the cuts in federal spending amounted to almost 18 percent of the money that would have been needed, with inflation factored in, to maintain service levels voted by Congress just before the 1980 elections.

"This report shows clearly that despite making speeches in favor of excellence in education, the president has been antieducation," Albert Shanker, president of the American Federation of Teachers, said at a news conference at the Sheraton-Washington Hotel. "If the president had done the same thing to defense that he did to education . . . the United States would not be a free country today."

In late afternoon Education Secretary Terrel Bell said parts of the union report "simply are not true." Bell scheduled a news conference today to discuss the union charges.

Yesterday's union criticism echoes the charges made against Reagan in mid-June by congressional Democrats that the president has "grossly misrepresented" his education policies.

Tom Fahey, a spokesman for the union group, said yesterday that he expected the new district-by-district data to be used as "campaign ammunition" in the 1984 elections.

The union report covers two major education programs--Chapter I (formerly Title I), aimed mostly at children of low-income families, and Vocational and Adult Education.

The report said 750,000 children nationwide have been dropped from Chapter I since Reagan took office. It said the president had sought to remove 2.2 million. The service levels financed by federal aid in vocational and adult programs have been cut by about 20 percent, it said, while the president had sought to cut them in half.

Locally, the unions said Reagan's proposals for the 1983 fiscal year amounted to a 45.6 percent cut in services under these programs in D.C., Maryland and Virginia, but it said Congress voted much smaller reductions than the president sought.

Actual federal spending on the programs in the three jurisdictions will be $153.2 million during the coming school year--about $720,000 less than two years ago.

In Washington schools, federal Chapter I aid was cut by $1.1 million last year to $13.7 million, but D.C. officials said they expect it to rise by slightly more than this amount in the coming school year.

The union report said the District lost $52.50 in Chapter I aid per school-age child over the past two years, more than any of the 50 states. But federal aid here remains relatively high--about 15 percent of the school budget--because of the city's large number of children from low-income families.

In Fairfax County, where the average income is much higher, federal aid covers only about 2 percent of a $449 million school budget. Yesterday Carl Juncker, the Fairfax schools' budget director, said the cut in Chapter I aid amounted to about $500,000 since 1981, some of which was replaced by local and state funds.