Depends how much you wish to spend in relation to the heli charter.
You've got Starspeed and Premiair at Blackbushe. As stated Fast at Thruxton, London Helicopters at Redhill and Alan Mann at Fairoaks.
As the selected final destination venue - I'm not sure where one would /land helicopter in the Hampton Court Palace area? There's the "Royal" Bushey Park that sits just to the north of Hampton Court Palace with the river Thames adajcent to the south.
The only other thing I can imagine is a pre-arranged private landing site located nearby within easy reach. Mindyou, now I think mabout it I suppose Sandown race track could be a possibility? Only about 10 minutes away by road.
Secret Service