Not at the moment. There is currently a restriction on which airlines are allowed to operate flights from LHR to the US. This is known as the Bermuda II agreement. Only BA, Virgin, AA, and UAL are allowed to operate from LHR to the states. There has been a great deal in the press recently about trying to secure an 'open skies agreement'. bmi are at the head of a 'make the air fair' campaign to end this 'legalised cartel'.
For more info, have a look at:
http://www.maketheairfair.com/
Hope this helps.
Barney