You can't be prosecuted for the same offence for which the caution was issued but there might be an additional matter to be considered.
For example, you could have said "Yes, I'm guilty of using threatening behaviour but I didn't hit anyone". That would enable the police to issue you with a caution for threatening behaviour but, if they believed that you'd also struck a blow, they would then have to pass the matter to the Crown Prosecution Service for them to decide whether there was sufficient evidence to pursue a prosecution for ABH.