There isn’t one as far as I know and it is set to get worse. The old Ocean Sky ramps that became part of Signature Terminal 2 are meant to become airliner stands in 2020 after modifications.
There is a large pocket of land to the south of the runway that is almost the size of the main apron that is still part of Luton that could be used just for biz jet storage. The problem is getting aircraft towed there which would mean crossing the runway but Luton’s runway is not always busy.
In the vision 2020-2050 document that looks at expanding the airport there is no mention of FBO’s
With regards to Gulfstream I did hear that they might keep a facility open at Luton once the bulk has moved out.