Many years ago, Hollywood and the Music Industry argued in court in the UK that since most UK ISPs have a mechanism to block stuff like child pornography, they ought to be compelled by the court to use this same mechanism to protect the interests of these commercial entities.
The courts agreed. If your ISP has such a capability the court will cheerfully give rights holders authority to demand the ISP blocks stuff that they claim rights over.
The ISPs could choose to just not block stuff. I am looking at Sci-Hub right now, because my UK ISP (Andrews & Arnold) doesn't block anything. From time to time, parliamentarians get vexed about this, but there is a cultural memory in the place that passing laws intended to stop people from saying things doesn't work. Lady Chatterley's Lover was banned, because, the government argued, it was obscene but it turns out that a court didn't buy this argument, and instead Penguin made piles of money because everybody wanted to read the banned book.
But most UK ISPs have decided that it is in their better interests to block things. Their options for attempting to do this have narrowed over time, once upon a time DNS blocking was pretty effective, I assume that by now they're mostly relying on IP blocking, which of course means they run the risk of exciting collateral attacks...
I don't know. Virgin Media quote High Court orders saying they have to block several I tried, but my home ISP does not block any of them. These seems weird to me, that the court orders would cover a few specific ISPs, but I haven't looked in to it further.
