At what point in time do you recognize the fact that placing your major airport in the western boundaries of your capital city, so that all flights have to pass over your capital city, was a major error in planning?
That's not strictly true.
When LHR was opened, ILS hadn't been invented and the piston-engined airliners that were around at the time used a Standard Beam Approach, which involved overflying the airfield, then an outbound leg with a procedure turn which, in the case of westerly operations, would take the aircraft over Brentford/Kew before becoming established inbound on the beam.
The need to be established at 8-10nm or more, thereby overflying central London, didn't arise until the advent of jet aircraft in the 1950s. Whether that arguably should have been foreseen in the 40s is a moot point, however as you rightly say we are now stuck with the consequences.