For further clarification . I should have consulted the definitive works on the ORBATs earlier.
It is now clear, looking at Josien's Orders of Battle and the summary in Nafziger, that 53 LAA Regiment which was the unit he went overseas with went to Egypt. This accords with the entry on "first half" 25 July 1942. So we have the beginning of his time overseas fixed.
The next embarkation (ie move on water!) was in August 1943 when his theatre changes from MEF to BNAF and later CMF which I submit m'Lud relates to the move of his unit to Italy. Thus we have the second part.
Seen the last page, think there is something missing entirely, it doesn't deal with discharge in UK.
I apologise for the bit by bit approach.
Caveat - as said before, I would really like to have seen the units in an ORBAT but so far have not worked through each of the formations in Italy although unfortunately, ORBATS tend not to show minor units such as transport companies.