Or perhaps flew from HKT to BKK then checked-in for the UK and went through immigration. As for "a flight from Suvarnabhumi to Phuket" you are the only one to mention that.
That is interesting. It was their booking form where I copied that text from. It also had the following which has to be acknowledged to proceed. Did you not have any of this on your booking form?
According to their website it would seem not;
"BFS Premium Airport Services provide “Premium Airport Pick Up Service” and we are unable to provide Fast Track to any passengers. Hence, Fast Track Coupons must be provided only by the airline.
Passengers traveling in Economy Class and passengers not holding Fast Track Coupons are required to pass through regular immigration lane where our BFS Premium representatives shall escort you further."
Wherever you go in the world you will find Filipino nurses, musicians, singers, cleaners, etc. You will rarely find a Filipino restaurant. There is a reason for that.