Surreyman
I grew up in Stanwell which is shown on the maps and adjoins the southern boundaries of LHR altho in those days it was open fields pre cargo centre. Stanwellwas in Middlesex as were Staines and Ashford
In the late sixties or early seventies Middx was done away with and most of it absorbed into various London boroughs but the area south of Heathrow became Surrey even though it was North of the Thames the previous Surrey Middx boundary.
At that time the bondary between Surrey and the GLC area became the LHR perimeter road until just east of Beacon road east of Stanwell where London started.
The western end is complicated because Berks (now Windsor and Slogh (Bucks) both have bits of land there but as far as I am aware Surrey neevr had any claim on any part of LHR itself.
PB