Iain, I know nothing about researching British vets, but until you get informed help, here are a couple of things I came across online.
BNAF appears to be British North Africa Force, and CMF is Central Mediterranean Force.
You said, "His military records only show his service record after the war." I wonder if it is possible you could get the remainder of his records? Perhaps info at this site would be useful: http://www.veteransagency.mod.uk/service_records/service_records.htmlhttp://www.veteransagency.mod.uk/service_records/service_records.html (You will note the link at the bottom of the page, "Veterans Agency Helpline". I wonder if anyone there could help you decipher 440A/44 and 2161A/44?)