If you book a through ticket from, say, BRS to LAX via AMS you pay the UK long haul apd rate. Here is a breakdown of a test booking I've just made with KLM, BRS-LAX via AMS. The UK long haul rate of £71 is clearly shown.
Price specification
adult
ticket price 278.00
carrier-imposed international surcharge 148.00
uk air passenger duty 71.00
uk international/domestic airport passenger service charge 21.73
airport passenger service charge 9.60
noise surcharge 0.80
security charge 10.40
us customs user fee 3.80
us international transportation tax 24.80
us aphis fee 2.70
us ins user fee 4.90
usa passenger civil aviation security service fee 3.90
usa passenger facility charge 3.10
price 582.73
number of passengers 1