With major help from the Reagan administration, Howard University has won an 8.4 percent increase in federal aid in the same giant budget bill and cut overall government spending by $35 billion next year.

The budget bill, which reduced spending for most federal education programs or kept it at current levels, was passed by Congress last week and now awaits President Reagan's signature.

Its new authorization for Howard -- $145.2 million in fiscal 1982 -- marks another milestone in the charmed political life of the university, which last year received more federal money than any college in the country except Johns Hopkins. Although Howard is a private university, the federal government pays about three-quarters of its academic expenses.

This year Reagan, while recommending 20 to 25 percent cuts in most education programs, sought a 14 percent increase for Howard. The president also met privately at the White House on July 9 with Howard's president, James E. Cheek.

Vice President Bush, who received an honorary degree at the university's spring commencement, personally spoke to several members of Congress in support of Howard's funds, according to the vice president's press secretary, Peter Teeley.

In late June, the Gramm-Latta budget bill, passed by House Republicans and conservative Democrats over strong protests from Democratic liberals, gave Howard everything Reagan requested. But the amount was eventually pared in a House-Senate conference.

"During the campaign last year, President Reagan pledged to help black colleges," Teeley said, "and this is a result of what the president promised. . . ."

"All in all, I think they did very well," said William Blakey, a Howard Law graduate who serves as counsel to the House subcommittee on post-secondary education. "Most [education] programs were held at last year's level or cut some, but Howard got an increase. It's not as good as they wanted. But they did better than most."

Howard officials said it was still premature to say which of their plans might have to be scaled back because next year's increase was trimmed from $19.2 million to $11.2 million. But congressional staffers suggested that some reductions might be made in the university's planned $15 million construction program, the $1.2 million it requested for radio, television, and film equipment, and its projected increase of 56 faculty members and 110 nonteaching positions in the face of virtually unchanged enrollment.

University officials maintain that all the increases are necessary to meet accreditation requirements, particularly for the many graduate-level programs Howare has added since the early 1970s.

The funds authorized by last week's congressional action still must be appropriated by Hill committees where approval is expected to be routine.