The M4 motorway now passes across the old Heston site, and Heston services is pretty much midpoint on the old airfield. The motorway opened in March 1965.
Across the Heston site the carriageways are in a cutting (you go up to the service area, and back down again on leaving, quite notably eastbound). Given that it took typically 3 years in those days to do the construction work and longer to do the land deals I would guess that mineral extraction in 1959-60 was being done immediately before the land was taken for the road, and was coordinated with the proposed carriageway earthworks.
There is still gravel extraction on the south side of the motorway between the two Heathrow junctions 3 and 4, which has been going n lackadasically for many years. The proposed new Heathrow north side runway will be there so it seems somewhat strange to be digging the ground out, it will presumably all have to go back.