You've probably found this entry in wiki about Old Dean:
http://en.wikipedia.org/wiki/Old_Dean wrote: When the estate was first constructed, the portion between the A30 and Upper College Ride, was littered with demolished concrete blockhouses and military installations. An "ideal" playground for the dozens of children who moved there in the early 1950s. These were once the barracks and training grounds of Charles De Gaulle's Free French Army and the connection is maintained in the name of the primary school: Lorraine takes its name from the Cross of Lorraine, from the French Region, the School's badge features the Free French insignia. When the School opened under the tutelage of Mr MacKean, the then French Ambassador attended the opening ceremony and read a message from General De Gaulle. In the early 21st century more affordable housing was added.
Google maps/directions suggest that it's currently around 7 miles from Chobham to Old Dean, but that includes travelling on roads that weren't there in the war. I suppose it would be possible for men to be billeted in Chobham but transferring them over that distance when they could be housed in temporary buildings closer to the training area seems a waste of energy.
However there were all sorts of wartime activities in the area:
This site may give you further leads.
Incidentally, I didn't know all this I just googled 'old dean common WWII' and 'Chobham WWII' so I'm sure that more intensive googling will give you more info.
Currently investigating the Hillmans of Sussex.