Welcome to pprune! I'm sorry, I don't know about the aircraft for hire at Fairoaks, but I am sure someone will have the info for you.
Alternatively, you could try Wycombe Air Park or White Waltham? Wycombe is junction 4 of the M40 and WW is at Junction 8 of the M4. These flying clubs have websites: Wycombe Air Centre, British Airways Flying Club, West London Aero Club.