Info from "Squadron Codes 1937-56", MJF Bowyer and JDR Rawlings. PSL 1979 ISBN 0 85059 346 6.
Both codes were used, DQ from September 1939 until late 1942, UE from 1944 when code letters were re-assumed by Coastal Command.
From December 1943 DQ was used by 551st FS/495 Fighter Group.
No confirmed use of UE by other squadrons before 1944.
From the above one could assume that the squadron's a/c were not coded.
From
www.rafweb.org
DQ Sep 1939 - Aug 1943
UE Jul 1944 - Jun 1945
Ciarain.