It's true, a police investigation may not go anywhere. I don't know how it works in the UK, but in the USA they would need to subpoena phone records, and to do that they will need to show cause (which is to say, they'll need to already have some basis for making the request). And even then, they'll may get some pushback (companies will suddenly decide that customer privacy is of paramount important at the oddest times). And all they might get is confirmation that texts or calls were made between two numbers-- no evidence at all of what was sent or said.
Then there is the effort of finding the people involved, finding anyone who might have seen or heard anything, and talking to as many of them as possible to see if a consistent/reliable narrative emerges. And, of course, getting the cooperation of those involved, especially the victim. If she decides she has 'moved on' or decides she does not want to go through the process, there isn't much the police can do. (And while it may seem sensible to expect the cops/DA to lean on the victim, you'd think differently if you've ever seen the effect it can have on a victim to try to relive the crime.)
Having pictures/copies of texts or recollections of calls/conversations is so flimsy from a legal standpoint that no DA worth his salt would even consider a case on those merits-- even if he feels that a crime was committed. Photos or video are much more compelling... but unless there is a clear smoking gun, you'd still need the victim's cooperation. Sometimes we need to remember that the court of public opinion has an extremely low bar for proving a case, which is why it's so unreliable (and sometimes so unfair).
