Loose end. Your interpretation of his regiment as 20 Light Anti Aircraft Regiment Royal Artillery (in UK Western Command in Sep 1939, NW Europe from Jun 1944) is correct but unfortunately doesn't help at all in obtaining his record, the system doesn't ask you to identify his regiment .
Follow Nanny Jan's advice in the post yesterday at 1903, check out the application form carefully, it has a detailed explanation of what they regard as next of kin.
MaxD