Horham and Thorpe Abbotts were constructed by civilian contractors, and certainly not by the RAF, as your web searches indicate
Did not mean that the RAF actually did the work themselves, rather they were built to a RAF contract. The RAF wouldn't have had the resources to do the work themselves, I doubt any RAF UK airfield was actually built by the RAF themselves.
There must be an act of parliament or legislation laying out the terms of agreement re USAAF airfields.
Interestingly found this re WWI.
http://www2.westsussex.gov.uk/learni...41e&version=-1