While some such stories could already be taken through a libel prosecution, others are not telling lies about an individual but simply based on an unreasonable amount of intrusion into their private life (hence interfering with their civil liberties). A recent example that horrified me was a media star, who, having been told of her sister's potentially terminal illness while she was many thousands of miles away, had to run the gauntlet of press/ photographers at several airports, and then outside her parents' house before she had even been able to speak to her sister. The Princess Diana road accident might also have been avoided if a law such as this had been in operation at the time. It might also avoid the ongoing psychological torture of other vulnerable young women whose fluctations in weight, spots, cellulite etc are continually featured in some publications- which also has the knock-on effect of lowering the self-confidence of the women who read such nonsense.
This problem has been raised quite a few times on this website, but it is obviously very difficult to balance the need for a free press against the horrific level of intrusion that is found within some tabloid publications. What if any story was open to a legal challenge of whether firstly it was 'over-intrusive' and secondly of whether or not it was 'in the public interest'? All such cases would have to be heard in open court, with no exceptions, to avoid abuses by powerful people (e.g., politicians trying to gag reports relating to their expenses!)
If a story was judged be 'over-intrusive' and not 'in the public interest' then the publication would be liable for the full legal bill plus any compensation awarded. Those under a certain income could be granted legal aid to pursue a case that was initially judged as having some substance (possibly in a short county court hearing).
This would mean that, at the publication stage, an editor would be entirely free to publish anything s/he felt was in the public interest, but that the publication would need to be aware that it might be called upon to defend any overly-intrusive story in court, and that they could be liable for a considerable sum if the case went against them.