Come to Boultbee Flight Academy at Goodwood. It's about an hour from London on the train and we have EASA instructors who can fly you in any or all of Chipmunk, Tiger Moth, Harvard (T6 Texan) or Spitfire.
Most Thrilling 50-minute Spitfire Flights over the English Channel
If you prefer to stay closer to London them I'm sure that WLAC at White Waltham can give you a great experience!
Happy landings!
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