Let me tell you how the system works:
1: If someone reports an alleged criminal offence, the Police are duty bound to investigate.
2: No Police Officer worth his/her salt would tell you to forget it. It is not their place to do so. Their duty is to gather any and all available evidence, be that from eyewitnesses, cctv, DNA, fingerprinting, by interviewing suspect(s) etc etc.
3: If anyone is arrested/interviewed as a suspect, the following course(s) of action may be taken: A) S/he/They may be charged with an offence and given Bail to appear at Court at a later date. B) They may not be charged immediately, but instead released on Bail to return to the nick at a later stage because Police enquiries are incomplete. C) The Custody Sergeant at the nick can decide to release them without any charge because of lack of evidence. D) Again, released without charge in the event that the complainant may decide to withdraw the allegation(s). E) A dossier of evidence gathered may be sent to CPS in borderline cases to decide whether the evidence contained in it is strong enough to prefer any charges.
Think very carefully before approaching the Police with such a complaint, because if it was a 50/50 type of assault, the other party may have as much reason to complaIn as yourself and the matter may ultimately fizzle out.