Uncle Peter you're nearly all there. The Thomas Cook frame belongs to ATrS, not the RAF, and is a damp lease. The other frame at BHX is entirely ATrS and crewed by them.
The SR pilots of ATrS are mainly ex RAF, but their T&C's are far from solid. Very few are actually AAR trained/current.
What they do outside the Mil contract is entirely up to them.
In times of actual war, who knows?