It's also probable that as He was at the Dunkirk Evacuation, He could have been either an Army Regular or Territorial in 1939, and might not appear on the 1939 Register, that was compiled primarily for the issue of Wartime Identity and Ration Cards.
I'm surprised You cannot obtain the Court Support Order, as it might be worthwhile Your Mother reapplying under the latest 'Freedom Of Information' Act. The services of a Solicitor might be worth considering. I believe obtaining sight of the Court Support Order, maybe the only way forward, with so little information, You have, on Your Mother's Father.