I have a few pages coveing the history of ATC at Ronaldsway, Isle of Man, from 1937 to the present day although I haven't yet covered military ATC in WW2 (mainly beacuse there are still major gaps in my understanding of it). Despite being first RAF Ronaldsway and then HMS Urley, the civil ATC continued right through the war years - there are some interesting surviving ATC Watch Logs from the time!
75 Years of Air Traffic Control in the Isle of Man
If you go to Elvington airfield just outside York (really worth the visit just for the aircraft) they have preserved the WW2 control tower and resored it to show operations at that time.
BTW - any corrections or additions to my web pages would be most greatfully recieved - is Ronaldsway the oldest continuously operation ATC unit in Britain? I think it may be.