I'm not sure exactly what you mean by "luxury goods", but if the value of your total purchases exceeds the current UK duty-free import limit of £390 then you will also be liable for VAT and duty at the applicable rate for the goods.

This will likely mean, given the pound's performance against other currencies over the past five years, you will be worse off compared to the Amex offer - the big c. 40% savings on electronicompany purchases in the US, for example, are long gone.