alt Hacker NewsClearcast is a private body owned by the broadcasters. The BCAP code is issued by the Advertising Standards Authority which, despite the name, is an industry self-regulation body.
It appears to be established in law that Clearcast is an assistance service, and approval doesn't seem to be sufficient or necessary by law to ensure advertising is legal. It establishes risk, rather than making a legal finding.
If Mullvad's ad was 'banned' by Clearcast, what happened is that their ad didn't meet the standards that the industry has set for itself and the broadcasters didn't want to touch it.
(edit - does this make it 'better'? I don't know. It seems to me a bit like the situation in the US with HOAs, which heavily restrict what you can and can't do with your property, but aren't exactly government either. But I favour accuracy over emotion when talking about this stuff, which is why I wanted to point out the actual structure of the system here.)
Not sure how an HOA is relevant here? Communities vote to form an HOA for themselves, new owners buying into an HOA community know up-front what the restrictions are.
Not remotely the same as a cabal of media conglomerates getting together to agree on their own rules about how they are going to interpret and enforce government-mandated censorship in society.