1943 London airport proposal

Fairey's 'Great West' aerodrome, named after the adjacent 'Great West Road', (nowadayscalled 'Bath Road') was situated just south east of the 'Peggy Bedford' Hotel, however the UK Airfield Guide website shows a section of a map published in 1935 showing an airfield called 'Heathrow' to the south east of this position and roughly where T4 now stands, so were there actually 2 airfields in this area? The map also shows the positions of Hanworth and Heston.
The website also explains that the name Heathrow was replaced by 'London Airport' on 25 May 1946 and reverted to Heathrow in 1962.

The Peggy Bedford was in a place known as Longford and it was nearer to the Great Western Aerodrome.

The Heathrow Aerodrome of the 1930's/1940's had been nearer to the old villages of New Bedfont, Hatton and General Roys Base Line.

www.ordnancesurvey.co.uk/blog/2013/11/he...general-william-roy/

Two different locations within the perimeter of the 21st century Heathrow.

I remember passing near Heston Airfield in the '60s & 70s and seeing a couple of hangars there with 'Fairey Aviation' on the roofs. One of these (next to the M4) later became the BA Social Club (late 70s). I also did a 2 week simulator course with BEA at Viking House, on the NW corner of Heston, in June 1974.
Did Faireys move to Heston from their 'Great West' aerodrome when Heathrow started to be re-developed?