At least 125 workers at Amtrak headquarters in Washington were abruptly dismissed from their jobs last week as the federally subsidized rail passenger system began instituting a 25 percent cut in its white-collar work force.

Anticipating a reducting of more than $150 million in federal aid for the 1982 fiscal year, Amtrak notified members of Congress that it plans to abolish 375 of the 1,400 headquarters jobs.Lawrence Gilson, vice president for government affairs, said in a letter to members of Congress that the reduction, through dismissals and attrition, was "part of our effort to reduce corporate expenditures to a bare minimum."

The Amtrak cutback was another indication that reductions in federal and federally subsidized employment under the Reagan administration will hit the Washington area hard. More than 5,000 federal employees in the Washington area are expected to receive dismissal notices this summer.

At Amtrak, the dismissal notices caught many workers by surprise and cost and jobs of career employes with many years of service, according to workers there.

An Amtrak spokesman -- who survived the cutback although five other persons in her department were laid off -- said the dismissals were "very difficult" because "these were perfectly capable people." To assist those who were laid off, Amtrak is sponsoring a "job fair," offering relocation assistance and paying employment-agency fees, she said.

Amtrak operates a nationwide network of 240 passenger trains serving 525 communities over 24,000 route-miles. It has used more than $5 billion in federal subsidies since it was created 10 years ago. Its total work force is about 22,000, but the only reductions definitely set are those in the executive offices at 400 North Capitol Street, according to Amtrak officials.

Amtrak's subsidy for the current fiscal year is $881 million. Amtrak President Alan Boyd said last month that all Amtrak routes could be made to pay their own way and federal subsidies eliminated by 1985, but he also said that Amtrak would need a subsidy of $853 million in 1982. It appears, however, that the actual amount will be at least $125 million less than that.