I'm pretty sure that the AIP states that you can only operate into LGW as a holder of a Commercial Licence and flying a twin (or more) engined aircraft.
I even believe for LHR that they're not accepting "Light Twins" - no definition you understand! - either (unless on Air Ambulance/Transplant work).
Please correct me if I'm wrong, but I think the days of Gatwick being the ideal place to stop and clear customs are long gone - shame.
I think I'd just operate into Redhill and pretend I'm landing on one of the "remote" Gatwick runways