The same flight, BA 223, was detained on the tarmac at Washington's Dulles International Airport on Wednesday for several hours shortly after landing.
FBI and Transportation Security Administration agents questioned passengers and crew for several hours aboard the flight and no arrests were made.
"We cancelled the flight for security reasons given to us by the UK government," the BA spokesman said. He did not give further details about the type of information given by the government.
A spokeswoman for Britain's Department of Transport said she was unable to comment on whether the cancellation was as a result of a specific threat.
The BA spokesman said alternative arrangements had been made for the 180 passengers on Thursday's flight, which had been scheduled to leave Heathrow airport at 10:05 a.m. (10:05 GMT).
Neither of the other two daily flights had been cancelled, the spokesman said.
Meanwhile an Aeromexico flight to Los Angeles from Mexico City was cancelled on New Year's Eve when officials, citing security reasons, said it would not be allowed to land, Mexican officials said on Thursday.
Aeromexico Flight 490 was originally scheduled to take off in the late afternoon on Wednesday but it was stopped after a call from U.S. Homeland Security officials, Agustin Gutierrez Canet, a spokesman for the Mexican president's office, told Reuters.
"The flight was cancelled and the 40 passengers that were programmed to fly took another later flight on Mexicana," he said.
The U.S. Department of Homeland Security in Washington had no immediate comment.