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.
The Croydon Park Hotel is just three minutes walk from the East Croydon railway station. It's about 15 minutes (£20) by taxi from Biggin Hill.