No right to free speech.
Then they start jailing people for posts.
Then they get rid of juries.
Then they get rid of public records.
What are they trying to hide?
They believe that they exist to control us. And let's been honest, British people are a meek bunch who have done little to disillusion them of that notion, at times positively encouraging our own subjugation.
In other countries, interference with the right to a fair trial would have lead to widespread protest. We don't hold our government to account, and we reap the consequences of that.
Free speech in the UK was done when people started to get police visits for tweets.
Don't forget your credit score being linked to how conformist you are.
The political answer is that open justice provides ammunition for their political opponents, and that juries also tend to dislike prosecutions that feel targeted against political opponents. See palestine action as a left wing example and Jamie Michael's racial hatred trial as a right wing example.
Obviously the government Ministry of Justice cannot make other parts of government more popular in a way that appeases political opponents, so the logical solution is to clamp down on open justice.
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I think there is a legitimate argument that the names of people who go to court and are either victims or are found innocent of the charges, should not be trivially searchable by anyone.
Though I'm not sure stopping this service achieves that.
Also - even in the case that somebody is found guilty - there is a fundamental principle that such convictions have a life time - after which they stop showing up on police searches etc.
If some third party ( not applicable in this case ), holds all court cases forever in a searchable format, it fundamentally breaches this right to be forgotten.