AMEX has a global transfer procedure through which you can apply for a UK AMEX card using your US credit. You need to have an existing US or other country AMEX card and have a UK address.
Also, you could open up an account with one of the multi-country "banks" like TransferWise and get a debit card that will support several currencies.
Echoing what others have already said--it really depends on why you want the UK card.