When William Killick boards his transportation plane to Greece the C-47 Dakota shows "D-Day stripes" (aka "Invasion stripes") on fuselage and left wing. Historically and consistent with the period setting of the story - the "Blitz" - this must have been in spring 1941. However, these markings were not in use before June 1944.
The air war scenes outside (as opposed to the opening film scenes in the Underground) purport to show London being bombed during the Blitz. The scenes actually were other film footage as Germany used no four motor bombers during the Blitz. The clip actually depicts British 'heavies' bombing Dresden by night near the war's end.
When William Killick boards his transportation plane to Greece the C-47 Dakota shows (incorrectly) black and white "D-Day stripes" on fuselage and left wing. In the stock footage (probably ex-RCAF ZA947 operated by the "Battle of Britain Memorial Flight") used for the subsequent takeoff shot the C-47 has no markings at all neither on wings nor the fuselage's underbelly.