I have not come across this family on the Killick mailing list yet, so unfortunately it does not sound familiar. This is some information on Robert according to Killick Society website and the Freebmd.
Birth Robert WalterKillick 1887 2 qtr St Olave (the Freebmd has his middle name as Waner)
Marriage Robert WKillick 1916 1 qtr Southwark
If you can send away for his birth certificate or find him on the 1891 or 1901 census. That should help you retrieve his parents names. I will look through what I have and see if he is in my files.