Hi there USdgUK,
Actually there IS something you can do, if you have an American Express card in the US. You can transfer your account to the UK operations of the company. Keep operating the account normally and they'll start to update the UK credit agencies here. That effectively becomes a 'shot in the arm' for you to build up UK credit.
If however you don't have a US Amex card, then as already said, you'll have no Credit History here and will need to start from scratch. Plenty of threads as well as the links above about it to help get you started. Get a low limit credit card from the bank you get with here and operate that well for some months, also a pre pay or substantial deposit on a mobile phone on a monthly contract will help too. These are just a couple of ideas.
Hope this helps a bit - Cheers, DtM! West London & Slough UK!