Just for fair balance, we're biased (obviously), but try Oxford (OXF/EGTK), often ignored in these threads but just won 'Best Business Aviation Airport' last week in European Biz Av awards, has 06:00 to midnight capability, seven days and has several daily G650 users already. An hour from London by fast M40 road or for crew 55 mins to center via Oxford Parkway station in Kidlington (new station). However, local HOTAC options excellent with many high-end hotels in just 5 mins drive from airport (Woodstock) or in Oxford (15 mins) at prices well below typical London-region costs. Helicopter shuttles offered at 22 min run to co-owned and operated London Heliport with 50% off fees if taken up as option.
On the costs front, OXF significantly less costly than most 'London' options and hassle-free, IS-BAH certified FBO (one of the very first), EASA-certificated airport, Gulfstream-OEM-trained handlers on ramp. Touch-down to leaving airport can easily be done in under five mins. MX support available too.