Looks like British Airways are codeshareing with bmi british midland on the Leeds/Bradford - Heathrow route and are offering world wide connetions via LHR.
The LBA to LHR point to point services are not bookable on the BA website but long haul connections are bookable. It also states that flights between LBA and LHR are operated by bmi uk domestic on an Embraer 145.
Flight details.
LBA-LHR
BD411 = BA7611
BD413 = BA7613
BD417 = BA7617
BD419 = BA7619
LHR-LBA
BD412 = BA7612
BD414 = BA7614
BD418 = BA7618
BD420 = BA7620