First his Army Number is in the Block alocated to the KOYLI, so you know he stayed with that Regiment.
1 KOYLI was in 15 Brigade, 5th Division.
I have their Div History. I'll look up exact detals if you like.
click>> 5th Division
Have a look here first though as it'd be easier for me.
click>> 1st Bn, The King Own Yorkshire Light Infantry: Deployments

They weren't involved in the battle for France in 1940 as they were sent to Norway instead with the rest of 15 Brigade. Then after that to India, Iraq, Persia, then into action on Sciliy, Italy, later to Anzio then back to the Middle east for a rest. Before going to Germany for the last from April to May '45.

To answer you queries on what the letters mean.

L/C Lance Corporal, the lowest NCO rank.
MT Sec would be Motor Transport Section, ie Battalion transport.
CMF = Central Mediterranean Force, see here.
click>> Allied Armies in Italy - Wikipedia, the free encyclopedia

EDIT--- It won't be WO Coy, it should read HQ Coy, Headquarters Company.

Let me know some specfic dates and I'll tell you where he was .
April 44 would be Anzio.

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