The thing about laws are they stop at the border. Unless you are sufficiently powerful that you can ignore the rights of other countries and their people, the UK isn't powerful anymore, but hasn't grasped that concept yet (I'm British, at this point it's just kind of sad).
So UK laws stop at the UK border.
4Chan is a US company, based in the US, with all its people and stuff in the US. It has never had a presence in the UK.
In the US people and companies have the right to free speech guaranteed under the first amendment, that includes speech conducted online. Many people would consider having the ability to speak, but having the government restrict hearing that speech to amount to a free speech violation.
The only jurisdiction 4Chan operates in is the US and they are defending their rights: they also have that right, the US isn't North Korea, or China, or the UK.
This isn't a matter of can they censor, of course they can. This is a matter of they don't have to, and they won't.
The UK has no jurisdiction, or reason to believe they have jurisdiction, or ability to enforce its laws extraterritorially over pretty much any foreign entity, but especially not the US.
Anyway you look at this, this is a jumped up little backwater not content with robbing their own citizens of their rights, they are now trying to rob others too.