The Justice Department notified several major airlines yesterday that it has begun a criminal grand jury investigation into suspected antitrust activities on routes between the United States and Britain.

Department spokesman Mark Sheehan said a grand jury sitting in Washington is expected to issue subpoenas "very soon" to the airlines that are subjects of the inquiry. The grand jury is investigating suspected violations of the Sherman Act.

Sheehan declined to specify the nature of the possible antitrust violations, but several industry sources said the investigation is apparently an outgrowth of the failure last year of Laker Airways.

Laker, the London-based discount carrier founded by Sir Freddie Laker, went bankrupt 13 months ago. The airline later filed a civil antitrust suit in U.S. District Court here, charging its competitors on the North Atlantic route with taking part in an illegal conspiracy to drive their upstart rival out of business. That case is pending.

Sheehan would not name any of the airlines to which subpoenas will be issued, but he said the convening of the grand jury followed consultations with the governments of Great Britain, Switzerland and West Germany. Airline industry sources said this indicates that British Airways, British Caledonian Airlines, Swissair and Lufthansa, the West German airline, are possible targets.

In addition, spokesmen for both Pan American World Airways and Trans World Airlines confirmed that they are among the subjects.

"We were notified this morning that they were going ahead," said Pan Am spokesman Jim Arey. "We haven't received a subpoena yet, so we don't know what they are going to ask for. We do feel there is nothing to indicate any wrongdoing by Pan Am."

A TWA spokesman, Jerry Cosley, said "we have had discussions with the Department of Justice on this, and we do expect to receive a subpoena." If the inquiry, which Justice began about the time the Laker suit was filed, does deal with what happened to Laker, TWA's position is that it is "pure fluff," he said.

Ironically, the demise of Laker did not put an end to cut-rate competition on the heavily traveled, highly competitive London route. Just two days ago, the Civil Aeronautics Board tentatively awarded rights to fly the route to Newark-based People Express, which is planning to offer a one-way fare of $149 beginning in late spring. British Airways' announced standard economy class fare at that time will be $440.

Sheehan said that the grand jury investigation was opened after Justice Department officials held two rounds of consultations with British government representatives to comply with guidelines issued by the Organization for Economic Cooperation and Development.