Hi Ramzy, and welcome to RootsChat!
Where did your grandparents marry?
The only marriage I can see on the GRO index for 1913 is between George E ARKWELL and Mary Elizabeth JOHNSON. (Mar Q, Lewes 2b 331)
This is probably the same George E ARKWELL who died Mar Q 1938 aged 65. (Lewes 2b 288)
However, George Ernest ARKWELL of Lewes (aged 42) gives his wife as "Frances E" on his WW1 pension documents in 1914.

There is no obvious birth registration in the GRO index, and no George Arkwell on census except the one Kerry found, unless he's hiding under a very bad transcription or something! Iis it possible that he was married twice? He would have been 40+ when he married in 1913, so it's not impossible.
Added: post crossed with lizb!Rambler