No, the ISPs who operate the ASes and routers that make up "the internet" are the ones who bring the service to the UK.

4chan does not reach out to UK users in any way, only responds to their incoming requests.

It really is analogous to UK users going to a foreign country, buying something that their home country has an issue with, having a third party ship it to their home country, and then their home country getting mad at the store.