Politics aside, how easy or difficult is it to block say X in the UK?
Politics elsewhere please. This is purely a question about technical capability.
For who and on what scale?
It's trivially easy to configure a DNS server to return NXDOMAIN for an arbitrary domain,
which is a common technique used to block shitverts, and would be a good way for a home network admin to prevent Friendface exfiltrating their browsing data.
It's approximately as easy to bypass a DNS server that blocks things you don't want it to.
On a network where you've got malicious users trying to circumvent the block (eg. a home network with teenagers, a business network or an ISP), null-routing the relevant IP addresses would be the next step. This is more of a game of whack-a-mole to administer, as you'd have to maintain the blocklist.
But ultimately, if the users have an approximation of a working internet connection, it's possible to run a VPN over it to somewhere that doesn't block whatever. (Does anyone have that link to the guy who was bored on a flight and wrote a program to tunnel over the airline's frequent flyer miles account data form?) In the UK, it's usually fairly easy for determined users to obtain an un-blocked connection via an alternative provider. (For example, an employer or educational establishment wouldn't be able to control what users do on their own cellular connections.) The old adage that "the Internet sees censorship as a fault and routes around it" has more than an element of truth.
At which point you end up changing tactic and concentrating the technical measures on *detecting* unauthorised use, and following up at a policy level (confiscating phones from teenagers, invoking HR on employees, suspending ISP accounts, sending the men in black round, whatever). This can include traffic analysis, proxying, deep packet inspection and similar techniques. The more effective ones tend to be expensive to implement at scale.
