scifi.. I am sure that my buddy Talkdownman and I could write ten pages on Heathrow sequencing but, basically, it's all decided by the controllers. Over the years there have been a number of attempts to "computerise" the task but none has been as efficient as brainboxes of highly trained humans. As TDM mentioned, the approach function was moved from the Tower building at Heathrow to West Drayton many years ago and subsequently moved to Swanwick. "Heathrow Tower" is the control room at the top of the tower which controls traffic on the ground and arriving flights from about 10 miles out. Outbounds are transferred to London Control as soon as they are airborne.
Details of all arriving flights appear on CCTV and the landing order is initially sorted to take account of wake turbulence categories to achieve the best landing order and to calculate expected approach times when aircraft are holding. In the end it is the Heathrow Directors who decide the actual landing order.
HTH