BA flights affected were three scheduled Saturday flights and Sunday's flight to Miami.
In Paris, Air France announced it is cancelling two Paris-Washington flights due to depart on Sunday and Monday.
"We cancelled these flights on advice from the UK government for security reasons," said a BA official, without giving details.
A spokesman for the government Department of Transport said: "In the light of information received, and in discussion with the airline, the decision was made that these flights should be cancelled."
"Aviation security is kept under review at all times... Aviation security measures are adjusted from time to time and occasional cancellations may be necessary."
"The first priority is always the safety of the travelling public," the spokesman added.
Intelligence information raising fears of a new September 11-style attack led to the cancellation of several international BA flights last month at the request of the US authorities.
Those cancelled flights included BA 223 to Washington as well as a BA flight from London to Riyadh in Saudi Arabia.
The British government warned at the time travellers faced years of severe security alerts amid fears by Western intelligence services of plots allegedly by al-Qaida and other groups.
BA also cancelled flight 263 to the Saudi capital Riyadh on 3 January because of security concerns.