It's certainly true that the UK libel laws are framed in such a way as to make it relatively easier for plaintiffs to win cases in British courts than in some other jurisdictions. Unlike comparable American laws, for example, it is not necessary to show that the defendant knew that the information they published was false, and yet chose to put it out anyway – in other words, that they acted deliberately and maliciously. Moreover, the defendant must be able to prove to the satisfaction of a jury that the claims that were made were actually true – not just that there was no demonstrable damage to the plaintiff's reputation – something that is typically very difficult when writing about people's private lives and personal relationships.
With regard to the British tabloid industry, which was at the peak of its success roughly between 1970 and around 2000, a period that falls within the parameters we're allowed to address at AskHistorians, the reasons for its ability to flourish despite those libel laws had a lot to do with two key factors – the power it wielded as the major, ongoing publisher of news in the UK, and the way that the British legal system charges costs.
To take the second point first, libel is a civil and not a criminal offence. This means that the plaintiff has to bear the costs of mounting a prosecution – the state does not do it for them. And, if the case is lost, the judge would typically "award costs" against the plaintiff as well, meaning that the newspapers' legal fees, which might easily run to six or even seven figures, would be paid by the person who had unsuccessfully asserted that they had been libelled. Since bringing any case before a jury can be considered risky – the members of the jury are human, they can be swayed by legal argument or their personal opinions of the plaintiff, and what the legal profession term "perverse acquittals" certainly do occur – it has historically been considered a risky thing to do. Moreover, the costs of mounting a case are typically disbursed while the case is being prepared for trial; law firms specialising in this sort of thing have never acted on contingency, taking a share of payments only in the case of a victory. Hence, only relatively wealthy people could even consider bringing a case against a mass-circulation newspaper – one that would have its own in-house legal team, and which could often attempt to spin out proceedings to make them intolerably expensive to a much-less-well-resourced plaintiff. Of course, a good proportion of the British tabloids' most notorious targets were wealthy celebrities, but very many, actually, were not, and a part of the tabloids' commercial equation, in such cases, was always the likely ability of their targets to sue.
The ongoing power of the tabloids was also a major factor in the ways their legal fortunes played out over the years. Celebrities, even if libelled, had to consider whether they could afford to make long-term enemies of newspapers that had circulations well into the millions – the notorious Sunday tabloid The News of the World peaked with sales of over 8m (and a readership several times that figure) in a country of under 60m people; The Sun and its bitter rival, the Daily Mirror, both sold around 4m copies a day before the rise of the internet. Such papers could do severe damage to celebrity careers if they chose to, and that was certainly a further factor in dissuading many people who felt they had been libelled from starting proceedings. This factor may help to explain the unwillingness of the British royal family (a major tabloid target for decades) to sue no matter what story was run about them.
A classic example of a tabloid libel case that illustrates all these points, which it falls within AH's rules to discuss, concerned the singer Elton John. In 1987, The Sun published a false story alleging that John had had sex with under-age male prostitutes. When it became clear that John would sue for libel over this report, the paper attempted to deter him by following this up with further stories attacking the singer – one of which alleged that he had had the vocal chords of the guard dogs used to protect his home removed to prevent their barks disturbing him. This latter story was relatively easy to disprove and John (who was of course more than wealthy enough to hire expensive representation) and his lawyers arranged things in such a way that this case was heard in court first. The impossibility of defending this claim forced The Sun to settle the case, agree £1m damages, and published a front-page apology to the singer. However, John and the newspaper subsequently took steps to repair their relationship and John frequently co-operated with The Sun after the case had ended, for example to publicise his AIDS charity.
Source
Peter Chippendale and Chris Horrie, Stick It Up Your Punter: The Uncut Story of the Sun Newspaper (2013)