Comment by ben_w
I believe the order of escalation here is:
1) Identify non-compliance or risk
2) officially request information from the website
3) wait for reply
4) formal enforcement proceedings: a fine and prep for court action (they are here)
5) convince a court to order the site to be blocked
https://www.ofcom.org.uk/online-safety/illegal-and-harmful-c...
Note that they themselves say there:
Where appropriate, in the most serious cases, we can seek a court order for ‘business disruption measures’, such as requiring payment providers or advertisers to withdraw their services from a platform, or requiring Internet Service Providers to block access to a site in the UK.
That sounds to me like they consider curtailing speech by blocking a website to be one of the last things to try, not the first.