Andymac,
Woodbridge was being used for some experimental work by the RAF with Lancasters being based there dropping Grand Slam bombs on Orford Ness, and the Blind Landing Experiment Unit was located there. Eventually it was closed on 14 March 1948 and put into 'care and maintenance' status. (Taken from Wiki)
RAF Cosford history:
DCAE Cosford - Cosford History
The only thing I can find (at the moment) on 236 Wing was that it was formed on 1 Feb '42 and was disbanded on 20 Dec '46. It's function is listed as mobile medium bomber / heavy bomber, which would tie in with the Woodbridge information above.
Taken from :
Royal Air Force Organisational History
Could the FC be something like Ferry Command or Facility Checking?
Perhaps give Hendon a shout too, although I agree with Cazatou that the Historical Branch will probably be your best bet. Write to them at:
Air Historical Branch (RAF), Building 266, RAF Bentley Priory, Stanmore,
Middlesex, HA7 3HH
Good luck - and when you find out, let us know too!
Brian
(closet historian)