Not all people who serve a website need to be aware of that - I don't think my personal blog will be declared illegal anywhere, for instance. If a post is, I might just spare myself the pain and remove it. If a country wants to notify me, I'm pretty easy to find.

Now, for a relatively high-profile website such as 4chan, who deliberately dodges responsibility for the content it knowingly hosts, I'd say it is not a huge effort. They have the staff for that kind of thing. If they decide they aren't complying, then the UK government might order UK-based ISPs to block access and they will comply - as they did many times before. The people in charge of the company might face charges if they ever set foot in the UK, but that's a risk they need to balance.

And, in the light of legislation that sanctions whoever does business with sanctioned companies, sanctioning advertisers can go a long way to force compliance.