What is the source of your information. ?
WW2 era U.K. service records aren't available publicly, they have to be applied for from the U.K. Ministry of Defence (MOD) for £30 and enough biographical information has to be supplied for the MOD to find and identify the record for the correct person, and if the person didn't die whilst in service proof of death must be supplied, which will usually mean a death certificate.
https://www.gov.uk/requests-for-personal-data-and-service-re...Royal Artillery attestation records up to 1942 are publicly available and they all contain service numbers, but there are 123 records for the surname Carr with a first forename that begins with J and 3 of those records only contain forename initials.
Did he survive the war. ?
If he did survive, the only way to find the info that you want is via WW2 Identity Card registrations, and that costs £42.
http://www.1911census.org.uk/1939.htm