With just 12 seats and one A380 flight a day, the BKK-LHR is regularly sold out in First Class 9-12 months in advance. It is also very pricey. Consider BKK-FRA/MUC/CDG and connect to LHR if you want to fly TG F. LHR, FRA and CDG.
For an additional fee, FRA offers a VIP transfer service where you are met at arrival flight, transfer by car over the tarmac to the VIP lounge where there is a private immigration, customs and security counters where there is unlikely to be any wait/queue. It is all very painless and gives a true First Class/VIP service. It is not expensive either compared with LHR or AMS for the equivalent service.