I understand one of the conditions of this is they are only allowed to carry "flight crew", ie pilots and engineers
That was certainly the case many years ago, certainly for ex military aircraft. Which is why Nick Grace said "No" when I asked for a ride in his Spitfire at a Middle Wallop airshow back in the 80s
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I'm not sure when it changed, but I finally got my ride in his aircraft a few years ago.
This is from "Operation of Permit-to-Fly Ex-Military aircraft on the UK register(2021)"
https://publicapps.caa.co.uk/docs/33/CAP632_E8_A2.pdf
Carriage of passengers
- 5.30 The Chief Pilot shall consider pilot experience levels before permitting pilots to fly with passengers. When passengers are carried, the Pilot-in- Command or appropriately trained person must deliver a suitable passenger briefing covering all aspects of flight including the use of safety equipment. The passenger briefing should include a statement that the aircraft operates on a Permit-to-Fly and is not certified to an internationally recognised standard.
- 5.31 When passengers are carried the operator shall maintain a record of the passenger’s name, address and next of kin details.