It's men who deserted from the Irish Army to fight in WWII that were refused benefits.
A deserter from WWI is British Army, many have received a pardon, not sure if all have yet.
You need to find his birth cert and his army record if it survived, but John Kelly is a common name so the place to start is his marriage cert which will hopefully give you his mothers name and a occupation for his father. I don't know how much info UK Certs have.
Look for the marriage here
http://www.freebmd.org.uk