Not really. US copyright law is based around protecting the rights to use a "work", but European copyright law tends to protect the originator. It might seem similar, but in practice it is not.
"Fair use" as an example, does not exist in the way defied in the US in the UK. We have "fair dealing" and it is a lot more specific. There are defined use-case exceptions to copyright, it is not "do what you like, claim 'fair use' and take it down when you get a DMCA notice".
