Absolute total longshot, but I can't think of any other way that you might achieve that.
Many ex servicemen from the WW2 era would have been members of the Royal British Legion, and the secretary of his local branch might have a membership record which might include his military details.
http://www.britishlegion.org.uk/ ...
http://branches.britishlegion.org.uk/branches/yorkThe only other possibility is if he married or had children whilst he was in service, servicemen sometimes included their service details on marriage and birth certificates.