Although there is a registration process in the US, use of it has diminished over the years. Also there is no requirement for a UK copyright holder to register and non-registration does not affect the existence of the copyright. However, it is my understanding that if you ever wanted to bring a claim for copyright infringement in the US then you would have to register them prior to bringing a claim. More importantly if they are not registered prior to the alleged infringement the copyright owner may not be entitled to benefit from statutory damages (up to $150,000 (and possibly lawyer fees) without having to prove any actual monetary harm).