Well, I am biased

, but on this I think the British have it right.
The First Amendment is a glorious thing, but I think modern press interpretations of it lean too far way away from conditions that permit a free and fair trial for accused prisoners. The poor deluded schmuck who confessed to the JonBenet Ramsay (I still can't type that without thinking 'what a stupid name! - that poor kid') murder recently was a case in point.
The before he'd even been brought back to the USA, his private life was paraded all over the papers and TV screens. In the unlikely event - given what we now know - that a prosecution had proceeded to trial, it would have been legal sophistry of the first water for anyone to honestly expect the jury to be able to make a decision on the facts presented at trial alone.
Our media is no better than yours, mind you. Indeed, they are worse; they are globally notorious for being nosily prurient. But our contempt of court laws are such that they are limited to being nosily prurient about entertainment and sports stars (who by the nature of their jobs these days have a symbiotic relationship with the press anyway) and about
convicted criminals (who, IMO, are fair game).
Suspected offenders cannot be named at all until they are formally charged, and in many cases, especially sexual offences, they can't be named until after they've been found guilty. Victims of crime, especially sexual crime, are also identity protected; unless they waive their rights themselves, it is illegal to print their names even after the case is made. (There are problems with the way the court system treats victims of violence here, but these mainly stem from the basic legal tenet that the court operates on behalf of the state, and not the victim; they are little more than a key witness for the prosecution. That's common to all forms of adversarial trial.)