Unless she made a statement to the police her evidence will not be admissible. The officer who heard her verbal version is not a witness to the events and he has no evidence to offer the court. He can only provide what is called “hearsay” (that is, second hand) evidence. Whilst hearsay is now admissible in some circumstances it is unlikely to be allowed here.
In saying that lots of assaults happen with no witnesses ummmm is quite correct. However, with the exception of domestic violence incidents (where the CPS sometimes adopt a different approach) very few, if any, are successfully prosecuted.
However, you should bear in mind that you are a witness to the events. I have to say that the police seem to have been a little lax in leaving it a month before interviewing your neighbour and this has not helped. However, the CPS may decide to proceed with just your evidence, but the chances of a conviction are reduced without the testimony of anybody else.
In common with all criminal offences there has to be evidence to support a conviction for assault. Contrary to what has been said, If there is no admissible evidence in the form of witnesses the CPS will not support a prosecution. After all, ask yourself if you would like to be convicted without any evidence against you.