Hi there,
I'd say if you are getting pre-approved US AMEX letters over there in the USA, then open one up - it'll be like you 'are in the USA' as far as AMEX are concerned. Operate it normally, use it as if you were there, purchase on US websites, settle the account in full each month - that way they'll build up your US credit report/history as well as with themselves in AMEX.
Then after some time, ring them to say you now live in the UK, and that you want to 'transfer' the AMEX history over here to help you get a UK AMEX card and then do the above, use it, pay in full each month and UK AMEX will already know you have a good history with them and start to update the UK credit reference agencies with 'good history' feedback from them and helping you to boost your UK credit score from them, as quickly as possible.
I think you'll probably run into trouble in applying for a new USA AMEX account with UK address and details as if it was a 'new' application - what with tighter lending practices at the moment and of course the whole issue with opening up bank accounts in different countries etc (much the same if I as a UK person, ring up MBNA, AMEX, BOA and say 'can i have a credit card please!')
Equestrian Nerd - 5X credit limit here in the UK compared to the USA one?! - summarises the UK's pathetic personal debt levels record really! - tip - to boost your UK credit rating (currently works!) ring up Amex and ask for a significant reduction in your credit limit - so perhaps if you have £15K of credit, ask them to chop it to £8K. Currently the credit reference agencies are looking at those who are actively appearing to be responsible with thier credit levels

Cheers, DtM! West London & Slough UK!