BA said on its Web site that flights BA 0873 and BA 0875 at 17:05 pm. Moscow time (13:05 GMT) and 21:15 (17:15 GMT) from Moscow's Domodedovo airport to Heathrow had been cancelled after police reported a terrorist plot involving up to 20 people had been foiled.
British Home Secretary John Reid said the alleged terrorists had planned to inflict a "considerable loss of life."
Police in London said the suspects had planned to bring explosives on board of planes in hand luggage and set them off on flights to the United States. Flights all around Europe into London have also been cancelled.
But spokesmen in the Russian capital said flights operated by Aeroflot from Moscow's Sheremetyevo airport and Transaero Airlines from Domodedovo airport were continuing according to schedule.
A spokesman for Transaero, which flies to London's second biggest airport, Gatwick, said the Russian government was yet to order a suspension of flights.
"Transaero [airline] will not cancel its flights to London without the proper orders," the spokesman said. "Our plane took off at 10.10 (Moscow time - 06:10 a.m. GMT). It is currently in the air and will land at Gatwick, where our planes usually land."
The British Department for Transport has already prohibited carry-on on board planes and banned almost any liquid - even bottled baby milk is subjected to restrictions - from being taken onto aircraft in connection with fears that the alleged terrorists were seeking to detonate a liquid-based explosive device.