If I try to go to thepiratebay.org I get this
--- Access to this website has been blocked under an Order of the Higher Court.
Any TalkTalk customer affected by the Court Order has a right under the Court Order to apply to vary or discharge it. Any such application must: (i) clearly indicate the identity and status of the applicant; (ii) be supported by evidence setting out and justifying the grounds of the application; and (iii) be made on 10 days notice to all of the parties to the Court Order.
For further details click here. ---
On top of that there is a voluntary scheme run by the Internet Watch Foundation to provide filtering for sites that share images of child sexual abuse. Some ISPs don't participate in this, but the vast majority do. One famous example of things that get blocked (but also reasonably quickly unblocked) are the Wikipedia page for a band. NSFW link https://en.wikipedia.org/wiki/Internet_Watch_Foundation_and_...