The Reagan Administration will cut off financial aid to colleges and universities with high default rates on student loans, Secretary of Education William J. Bennett threatened yesterday in a Washington press conference.

Higher education lobbyists--longtime antagonists of Bennett--vigorously opposed the plan, saying it was another Reagan attempt to hurt colleges and universities.

The soaring numbers of students who fail to repay their loans has shocked congressmen and sent Administration and college officials running to find a solution. The government's annual payment on defaulted loans will jump 10-fold from $209 million in 1978 to $2 billion by the end of the decade.

"Defaults have continued to soar to levels that are intolerable," Bennett said yesterday.

"This is a disgraceful situation no one, neither Congress nor the executive branch, intended," said Bennett.

Under the Bennett plan, schools at which more than 20 percent of those students with GSLs fail to repay their debts will lose access to all federal financial aid programs, including Pell grants and College Work-Study. The plan, which does not need Congressional approval, will impose its first cuts in 1989, the Secretary said.

Bennett has sent letters to the presidents of all colleges and universities that participate in the GSL program, notifying them of the scheme.

Education lobbyists representing Harvard and most other colleges and universities have waged a battle to pre-empt Bennett's plan by proposing their own solutions to the default problem. They fear that Administration officials will use the default issue to achieve their long-sought goal of crippling financial aid programs.

"Bennett and hostile congressmen could use default to threaten funding for all financial aid programs," said