I was assaulted by my next door neighbour in Tamworth uk and…

There is a common misconception that it is a victim that presses charges. It is not the victim that presses charges, but it is the police that bring the charges and it is the victim that supports them with a witness statement and all the witness statements, preferably from independent parties etc.
The police will only a refer a matter to the CPS and the CPS will only bring a prosecution if they can prove beyond all reasonable doubt that the offence was committed.
It would appear that the alleged attacker is saying one thing and you are saying another.

Unfortunately, the attacker has come up with an “independent” witness whose version of events support his. I appreciate that the witness may be known to the attacker but the police will not carry out in-depth investigations into that relationship unless you go to them with some kind of evidence that the witness is not being 100% truthful.
This decision not to investigate it is purely based upon public interest, whereby they will not spend unlimited re-sources investigating matters which may ultimately go nowhere.
Based upon the information that you have given me therefore I think the only course of events that you can follow is to write to the chief Constable and complain.
Even so, I think it most unlikely that the police will refer this to the CPS and the reason for that is that, based upon the information you have supplied , there is not a good chance of proving beyond all reasonable doubt that the incident occurred without provocation.
I completely accept your version of events is being 100% correct, but unfortunately it would be for the court, faced with two completely different versions of events, to decide which one they preferred and in these circumstances, it would be impossible for them to do that and prove the case beyond all reasonable doubt.
I am sorry, I appreciate that this is not the answer that you wanted but I am sure that you would prefer an honest answer and not one which was misleading.