The Director of Public Prosecutions can appeal the verdict but this rarely happens.
Essentially the jury were not convinced "beyond reasonable doubt" (a very high standard) that the accused was guilty based on the evidence presented to them. Unless there was a clear and demonstrable flaw in the trial process there is little that can be done. If there was such a flaw it is unlikely to have gone unaddressed by the prosecution in the trial.
Previous convictions are not usually admissible as part of the prosecution case. There are now facilities to introduce them if the defendant has a clear propensity to commit similar crimes, but this is exceptional rather than the rule.
Usually medical evidence supports the level of injuries sustained but can rarely prove who inflicted them and very often cannot show exactly how they were sustained.
It probably does not help, but you refer to "your friend's GBH" case. It is not hers. It is brought by the CPS and she is the victim and a witness. Decisions regarding the conduct of the prosecution (and any appeal if appropriate) are for the CPS to make.