There is a general principle of the court publishes a fair, accurate and contemporaneous record except where this would create a substantial risk of prejudice. Here are the details https://www.judiciary.uk/wp-content/uploads/2015/07/reportin...
These UK reporting restrictions are also why the BBC (and other major UK-based media) are very careful about how they report on criminal proceedings.
Looks like the difference is that there's no jury to be prejudiced, because trials are decided by the judges only.
I wonder though if the extradition request is going to be decided by the jury at some point, in this case in particular.
It should be pretty obvious why.