Whiskey Oscar, there are two major defence contractors in the UK who employ civilians to fly for jobs supporting the Armed Forces. One is Hunting and the other is Flight Refuelling Aviation (who do a great deal more than just flight refuelling - it's an old name).
Hunting run the Joint Elementary Flying Trainnig School, the Skyvans at Oxford for parachute training and the Hawks at Culdrose. FRA run the EW training contract at Tees-side, various target facilities operations, and the military airfield instrument approach aids calibration contract.
However, both firms take only experienced pilots, the majority of whom are ex-military, so these are not really jobs for wannabes.
All the best
Paul