You asked if anyone has ever taken a light single into Gatwick. Yes, but so long ago. In the '70s one could easily use their GA terminal to clear customs and pick up or drop passengers. I must have been in there at least half a dozen times, probably cost about £3. Those were the days!
Not much use to you now, but please, please, let us know how you got on and the cost on your landing there on Thursday. I might try it again just for buzz.