[Nick Beale]

There have been other threads about this but here is the position for 1944:

British:

16 September 1943 – 1 April 1944: British Summer Time (GMT+1 hour)
2 April - 16 September 1944: British Double Summer Time (GMT+2 hours)
17 September 1944 – 1 April 1945: British Summer Time (GMT+1 hour)

German:

4 October 1943 – 2 April 1944: Central European Time (GMT+1 hour)
3 April – 1 October 1944: German Summer Time (GMT+2 hours)
2 October 1944 – 1 April 1945: Central European Time (GMT+1 hour)

In the one example I have, local time was kept aboard HM ships.