Reinforcing its pledge to support higher education, the House of Representatives is expected to approve legislation tomorrow that would boost funding for student financial aid programs, Congressional aides said yesterday.

The bill, as reported out of the House Appropriations Committee last week, would increase funding for the Education Department by $1.1 billion, to $20.6 billion. Financial aid programs would receive more than $323 million in new money, said a Congressional staff member.

The increase would be only half of that permitted by the joint budget resolution Congress approved in May. However the bill, if approved by the Senate, sets spending at a level about $6.6 billion higher than the Administration's budget request and may face veto by President Reagan.

"This move shows that we will not let education down," a Congressional aide said yesterday.

Many Congressmen believe that support for financial aid and other higher education programs is essential for building a trained work force capable of handling high technology. Such ability is critical for improving America's faltering position in international trade.

"[Congress] has done a very good job," said Charles Saunders, vice president of governmental relations for the American Council of Education (ACE), an umbrella group representing most colleges and universities in the country.

Working closely with the ACE and other higher education associations, Harvard officials have lobbied heavily on Capital Hill for increases in financial aid funding. Last year, more than 2000 Harvard undergraduates received some form of federal financial aid, in the form of loans of outright grants.

Almost 540 Harvard students last year received Pell grants, which the House bill targets for the largest funding increases. The legislation would increase the average Pell grant, which is provided to low-income students, from $2100 to $2300. Special programs that encourage minorities to attend colleges and universities would also be big beneficiaries of the legislation.

The House bill also would double the funds available for graduate student fellowships, and would boost campus-based programs such as College Work-Study. Funding for construction of campus facilities and the purchase of new library technologies would receive moderate increases.

Education Department officials, led by Secretary William J. Bennett, have criticized sharply Congressional increases in funds for colleges anduniversities. They have repeatedly termedCongress' spending decisions "reckless" and"wasteful," and have tagged America's colleges as"greedy."

However, in June the Administration beganleaking rumors that Bennett would no longer seekthe deep budget cuts that Congress has rejectedfor the last six years. Citing the influence ofthe new Chief of Staff, Howard Baker, Departmentofficials have said they are currently consideringa budget similar to the House appropriations billup for approval tomorrow.

Baker and his aides argue that the budget cutshave handicapped Administration efforts to get itsother education ideas, such as new loan programs,approved by Congress, sources said last month.

Some Congressional aides and EducationDepartment sources believe that the change inpolicy has occurred for political reasons, as theAdministration budget proposals will appear justin time for the 1988 primaries. However, highereducation officials are more dubious.

"Big deal, what are we supposed to do, jump upand down in anticipation?" Saunders said. "Are wesupposed to be grateful that [Bennett] is onlygoing to cut us 15 or 20 percent instead of 50percent?