Cost and Complexity.

It would require a major reconfiguration at LHR to set up a pre clearance facility that is equally accessible to ALL airlines.

There would need to be a Treaty between the US and UK governments followed by legislation in Congress and Parliament to pass the necessary laws and regulations.

IIRC it is US policy that the other nation / airport pays for all the capital costs of the necessary equipment and compensates the US for the additional costs of posting CBP officers oversears over and above the usual costs for a 'normal' US landing.

I don't see HMG paying and LHR will have reservations and there will be a slew of airlines who will refuse to contribute a penny towards the cost of a facility / service they will never use either by the landing fees or passenger service charges.

There would also be implications at some US airports. Could JFK T8 domestic facilities handle over a dozen BA/AA flights a day without needing more baggage handling space etc.