Hi Colin, here`s some info i came up with that should help you.
ARMY AIR FORCES STATIONS
A Guide to the Stations Where U .S . Army Air Forces Personnel
Served in the United Kingdom During World War II
by
Captain Barry J . Anderson, USAF
Research Division
USAF Historical Research Center
Maxwell Air Force Base, Alabama
31 January 1985
http://www.afhra.af.mil/shared/media/document/AFD-081010-027.pdf
Quote from the .pdf :
Airfield construction can be divided between a small number built by
U .S . engineers and a greater number constructed by the British . American
aviation engineering battalions built Andrews Field (Great Saling), Birch,
Boreham, Chipping Ongar, Debach, Eye, Glatton, Gosfield, Great Dunmow,
Harrington, Matching, Nuthamstead, Raydon, and Stansted (Mountfichet) .
Harrington was constructed for the RAF in exchange for Little Staughton,
built by the British for the USAAF .
From a Wiki page on RAF Birch :
http://en.wikipedia.org/wiki/RAF_Birch
Overview
Birch Airfield was allocated in August of 1942 to the United States Army Air Force Eighth Air Force for development into a heavy bomber base but construction work did not get under way until well into 1943. In October 1943 the base was transferred to the Ninth Air Force.
Birch was constructed by the 846th Engineer Battalion, U.S. Army, and it was the last of the UK airfields to be completed by a unit of the U.S. Army.
Looks to me like the British airfields after 1943 were built by the RAF Airfield Construction Service.
Units of what became the RAF Airfield Construction Service in 1943 built 23 Advanced Landing Grounds in Kent, Sussex and Hampshire from which fighter and fighter bomber squadrons were able to operate over the Channel and the D-Day beaches.