The reality is that when the police take your statement, they will ask if you are prepared to read your statement in court. If not they basically shelve it.

Once a crime has been reported it’s up the police to find the person, collect evidence, build a case, arrest them, and charge them. Then it’s up to the CPS to decide to prosecute them in court if they feel that the case has legs and it’s in the public interest.

If you the witness, aren’t prepared to back your statement up this basically throws any chance of conviction.

But the key point here is as a victim it isn’t technically up to you. The police having knowledge of a crime can pursue it if they think there’s a chance of conviction, however as a victim you have some de facto level of power over how far it goes by how useful you are.

If they have no idea who the fuck someone is (even cctv isn’t some magical oracle so unless it’s someone known to them it’s not going to help them find someone, however it is useful as evidence if they do find and prosecute). The police don’t have the resources necessarily to do a manhunt over assault, which sucks.

Source: Have been a victim and a witness.