That's the judicial system (not "the government") that decided that someone's privacy was more important than having their private life all over the street (which was hardly directed at the BBC, but more the tabloids).
You can of course argue about these things and where the balance should be, but most of these cases are little more than "some vaguely famous person fucked someone" and are not really "in the public interest" as such. Certain sections of the British press seem to think that you have no right to any privacy at all after you've appeared on TV two or three times.
To summarize that with "the BBC is regularly censored by the government" is quite misleading.
https://en.m.wikipedia.org/wiki/Super-injunctions_in_English...