Bryan, according to Amazon, the Blu Ray format released here in the US is "Region A/1."
See the breakout below regarding the different formats. If I read this correctly, it is not "region free" and the format you would purchase through Amazon UK will be different than mine. So I don't think they are compatible.
Region A/1: North America, Central America, South America, Japan, North Korea, South Korea, Taiwan, Hong Kong and Southeast Asia.
Region B/2: Europe, Greenland, French territories, Middle East, Africa, Australia and New Zealand.
Region C/3: India, Nepal, Mainland China, Russia, Central and South Asia.
"There's nothing in my bedroom that bothers me."