Hi frimleypicker and others,
not sure if you still look at this site as this is such an old post, but I may have solved your mystery!
I lived in Byfleet in my younger years and when I started driving, at night park up in the BAE carpark and hangout with mates.
At the time I heard rumours of tunnels under the carpark but only found out recently they were in the chalk sides of the old sand pit.
Well. digging around I found this vid on youtube:
Interesting video.
and in the description it makes reference to the tunnels being used as a medical centre after the war as in the quote below.
"After the war the area including the hanger and the tunnels, was used as a Medical Centre, vehicle servicing and staff car parking. "
Hope this is helpful and clears up the mystery?
Cheers