Each country's banking regulations are quite different, and international banking can be particularly onerous.

With all that said, good ol' PayPal may be your easiest answer if it supports the common UK and EU payment platforms you need.  It's easy to integrate into a website.

You can also check out Authorize.net - the credit card handler we used before we transfered everything to the HomeAway credit card system.  I somewhat recall when we openned our merchant account with them that they were supported in countries outside the US.  I know I really liked their virtual workstation that let me enter the CC info and track payment histories, etc.

Although probably not ideal for your situation, but of use to others who may be reading this thread - a couple of well-respected international payment systems that can be added to a stand alone website are:

Google Checkout: https://accounts.google.com/ServiceLogin?service=sierra&ltmpl=seller&continue=https://checkout.google.com/merchantSignInRedirect

Amazon Checkout: https://payments.amazon.com/sdui/sdui/business/cba