And a legal minefield. The "citizens arrest" power only applies where an "arrestable" (a legal definition) offence has been committed. As far as assault goes, this includes ABH (Actual Bodiily Harm) and above but not Common Assault which this seems to be. If she had complained and pushed it, you may well have found the police would have had to report you for unlawful arrest.
For peep's information: ABH requires a "significant" or "actual" injury - good black eye, split lip, substantial bruising, small cuts, etc. - something which interferes with the health and comfort of the victim (probably needs first aid / A&E). Common Assault would be "trivial" injuries, things which disappear in a few hours and probably need no treatment at all (e.g. tiny bruises, reddening from slaps, grazes, etc.)
Before anyone asks, the police do have additional powers, over and above what we citizens have.