I initially wanted to use Liquid Web but since they charge in USD, my bank doesn't let me pay them.
Are there any other companies in the UK that you'd recommend for AM purposes?
I don't see any reason why you couldn't pay a company that charges in a different currency, your bank will simply use a conversion rate and that's about it. I'm doing this all the time for currencies different than US and EUR ... no business can have accounts in all currencies that they need to work with. If your bank refuses to do this for you, it's time to look for another bank.