People Express Airlines yesterday won Britain's approval for its $149 trans-Atlantic fare, and last night sent its first low-cost flight winging from Newark Airport, outside New York City, to London. Its fares are about half of the lowest price currently offered by other scheduled airlines.

There were no special ceremonies marking the maiden flight for the two-year-old Newark-based airline, which is making its bid to succeed where Sir Freddie Laker failed in offering low-cost, no-frills flights across the Atlantic.

People Express will charge passengers on its domestic Newark-bound flights $20 to connect with its trans-Atlantic flights, making the Washington-London fare $169 each way. The airline, using a 747 jet leased from bankrupt Braniff Airlines, will make five round trip flights a week between Newark Airport and Gatwick Airport, just outside London.

So far, People Express officials said the response has overwhelmed the airline's already jammed reservation phone lines. Airline spokesman Russell Marchetta said all 390 economy seats on last night's inaugural flight were filled despite the short time to plan for it.

Moreover, Marchetta said that the airline sold 8,400 tickets Monday, the first day they were offered, amounting to more than one-fourth of the 34,000 seats available on its flights through September 13. Major holiday weekends, such as the Fourth of July, were completely sold out.

People Express began selling tickets in an effort to demonstrate public support for its flights to the British Department of Trade, which had linked its approval to a U.S. Justice Department investigation of possible criminal antitrust violations arising from the Laker bankruptcy.

The Trade Department, however, gave its permission yesterday morning for the People Express service to start "forthwith" after two days of talks in London with U.S. officials

There was speculation here and in London that the British were trying to pressure the U.S. government to drop a criminal antitrust investigation of charges that Laker's competitors on the trans-Atlantic route had conspired to drive him out of business. The trustees of Laker's airline have filed a civil antitrust suit in U.S. District Court here making the same charges against a number of his competitors--including British Airways and British Caledonian Airways, who last week lost their bid to have the case transfered to British courts.

Lord Cockfield, the Trade Department's secretary of state, said yesterday that People Express' application was considered "in the context of discussions between the British and American governments about the application of the U.S. antitrust laws to British airlines, which has created great uncertainty about their ability to compete with operations such as those of People Express.

"Encouraging progress in those discussions has now enabled the British authorities to process the People Express application expediciously," Lord Cockfield concluded.

British Embassy officials here said no deal was made in the Anglo-American talks and a Justice Department spokesman said there was no linkage between the discussions and its antitrust investigation. The British, he said, wanted to know more about American antitrust laws and how they applied in the context of People Express.

The People Express $149 Newark-Gatwick fare compares to the regular one-way trans-Atlantic coach fare of between $355 in the off season and $440 in the summer. Airlines also offer standby fares of $350 and a special $549 round trip fare with certain restrictions.

It is about the same as the $135 that Laker charged when he began his "skytrain" service between New York and England in 1977. He declared bankrupcy in February, 1982--brought down by the recession, high interest rates and a drop in the value of the British pound, which increased his dollar debt. His fares had jumped to above $200 by the time he went out of business.

People Express also offers 40 "premium class" seats, which cost $439 compared with regular first class charges of $1,929 and business class fares of $956.

But People Express travelers in either class will have to buy their food and drinks and pay a small surcharge for checked luggage.