This is as far I got with the rumour, from the last update of my 'Whispers of War' article (http://www.psywar.org/sibs.php
An example of one of the really bad rumours concocted by the UPC and which was severely ridiculed by the Air Ministry said that in a Messerschmitt fighter brought down recently, some of the rivets were found to be made of wood! It seems the UPC had a preoccupation with wooden planes, suggested in January 1941, another of their rumours joked:
The Germans built a dummy aerodrome in Normandy with wooden planes. Next night the RAF bombed it – with wooden bombs!15
The sib was not approved for dissemination, since the ISSB considered it liable to compromise intelligence sources. The joke, however, appeared in print a few months later in the CBS correspondent, William L. Shirer's book, Berlin Diary: The Journal of a Foreign Correspondent, 1934-1941. Under the entry for 27 November 1940, Shirer claims he heard it from a mysterious source referred to only as "X" but this time the location of the dummy aerodrome was near Amsterdam. It is now impossible to tell whether PWE supplied this amusing anecdote to Shirer as filler for his book, or if it was Shirer who got the story in circulation after his return from Germany. Either way since the war it has become an urban legend in various guises.
So either 1) Shirer first heard the story in Berlin in November 1940, which then somehow also got back to London by January 1941...
Or 2) the UPC made up the story in January 1941, it was blocked for dissemination, then the UPC modified the location and planted it on an unsuspecting Shirer when he was preparing his 'Berlin Diary' for publication in, IIRC, June 1941.
Not sure if it's relevant or not, but "X" happened to be the code letter for the German section of the Special Operations Executive. However, in theory, SOE's department D/Q were responsible for spreading the rumours, not "X" section.
Version 2 is just speculation on my part and perhaps I should remove my tin-foil hat
- Editted to add, All sides did use wooden decoys of aircraft, tanks, etc. but I do not suspect for one moment that the RAF actually dropped wooden bombs on any wooden aerodromes; it was just a good story and typical of British humour.