Prince Harry's libel case against the Daily Mail, News International and The Mirror Group newspapers was very revealing. He exposed that the tabloids operate like the mafia and if anyone took them on they would investigate them to look for any dirt in their past and publish it in their paper. So if they ran a story against a prominent celebrity who subsequently attempted to sue them with libel, they would threaten to expose further stories about them so they would back down. When politicians have tried to toughen laws to stop the papers from employing illegal means to get stories and to improve the mechanism by which wronged parties can seek redress, those papers have been ruthless in attacking those politicians and supporting opposing political parties and as a result, they have always backed down.
The closest we get to curtailing this behaviour was when Ed Miliband was leader of the Labour Party and he forced the Conservative government to hold a public enquiry into the tabloids. The inquiry was to be in two parts: Leveson 1 and 2, named after the judge who headed the inquiry, Leveson 1 was completed but the government failed to implement all the recommendations and scrapped Leveson 2. Jeremy Corbyn, when he became Labour leader, promised full implementation of Leveson 1 and to push ahead with Leveson 1. The tabloid unleashed holy hell against him and were vicious and relentless in their attacks on him . Sadly he lost the election so little changed and Leveson 2 never happened.
Prince Harry's libel cases against the print media has meant that the tabloids recently have been more careful with their tactics because he showed that mistakes can lead to the papers being forced to pay out huge financial penalties. However, most people do not have his resources so the tabloids will still go after certain targets.