Hi jjoes: In summary, often in cases of (minor) assaults where witness / victim evidence has been withdrawn the prosecution offer 'no evidence' and the case is discontinued.
However, this offence falls within 'domestic violence' and most forces will robustly pursue DV incidents with a view to prosecute. Also, DV offences are commonly considered to be in the public's interest to prosecute and the CPS (Crown Prosecution Service) and Courts commonly hear DV related cases even where victims have withdrawn their complaint.
The problem with the case as you have described is that the accused has made admissions during police interviews. There was an initial complaint of unlawful assault and corrobation by way of injury, although, true corroboration is proving that the accused caused the specified injury and that it was unlawful. (basic terms). Without expert medical evidence, ABH would appear to be the appropriate charge. On the facts you have disclosed I would agree that the defence are 'hoping' the case will be discontinued on the grounds of no victim / witness complaint etc but your brother needs to confirm with this with his solicitor and what to do should the prosecution continue.
This is a summary reply as there are numerous factors to consider in such cases but this gives an insight into DV related cases etc.
dh