There's a very good database https://www.bailii.org/ that hides itself from Google. But that doesn't have everything, just the most important cases.
> There are very complex restrictions on reporting
These badly need reforming for the 21st century, but, like a lot of the courts system, which is simultaneously inefficient and badly funded, nobody's going to touch it.
It's quite a useful (and fascinating) site and I've browsed it a few times before. But a limitation is that it just has copies of written judgements. Contemporaneous reporting of trials, particularly criminal trials, can give quite a different insight, especially for those cases which are not as high profile as those which go to the Old Bailey.
> There are very complex restrictions on reporting
These badly need reforming for the 21st century, but, like a lot of the courts system, which is simultaneously inefficient and badly funded, nobody's going to touch it.