For what it's worth...
Our operation finds Biggin to be the best London area airport for ease of use, not just cost. Luton has got very busy, the service from the 'new' Signature FBO at Luton is shambolic. The only benefit of Luton for us (and you guys) is that Gulfstream are there. If you can plan some maintenance whilst visiting, and are on Gulfstream's apron or in the hangar you will not pay parking fees. Harrods Aviation are now our preferred handler at Luton.
When Rizon Jet had an FBO at Biggin Hill, it was second to none. Signature have since taken it over, and ruined it. The service really slipped.
The choice at Biggin Hill nowadays is Signature or Biggin Hill airport handling. In the past, immigration have visited the aircraft when we have used Signature. I'm not too sure whether they will visit the aircraft if you use Biggin handling (the airports own handling). I seem to remember that customs/immigration had a desk as you enter the terminal.
The airport is planning to add an RNAV approach soon, in addition to the ILS on the other end. Operating hours have recently been extended.
There are many options for crew hotac nearby. Signature (and Rizon Jet in the day) seem to prefer the Croydon Park hotel, it's a bit run down but fine for a night or two to be honest. The hotel is a five minute walk in to town. There is a Hilton and a Ramada nearby also. London is easy on the train from a station five minutes away from Biggin Hill.
I'm not 100% sure about the tax free item's, but certainly in the past this was possible.