The RAMC operated a system of trickle posting, that is to say, men were moved individually between units as required, either to fill specialist roles or for career advancement/promotion, so that means that he didn't necessarily spend the whole war with 11 Armd Div. Indeed between its formation in 1941 and D Day in June 1944, the division spent most of its time in the UK in training and wouldn't have needed full RAMC support. So Sgt Barker could easily have been serving in the Far East up until 1944 or perhaps later.
It is hard to be certain which medal ribbon he is wearing. It looks as if it could be the
France and Germany Star which would accord with him being in 11 Armd Div. However he doesn't seem to have been entitled to any other medal such as the Burma Star. To qualify for the Burma Star he would have needed to have served in that theatre of war after 11 December 1941.
If you can get to the National Archives at Kew the war diaries for 11 Armd Div Medical Services are held in
WO 177/371