ok - lets break this down.
S.39 OAP - a s.39 is a battery offence, which, unlawful touching is enough to commit a battery. So, yes - if your son pushed the 'victim' out of the way, he is guilty of a s.39
HOWEVER - no Magistrate in this country is going to hand down a custodinal sentence for a simple push, this is where the 'rendering unconcous' bits comes into play.
If i've read it correctly, and please state otherwise if I haven't -
The Police had a admission off your son for pushing the guy out of the way, and your son has a witness of this taking place.
Yet, no-one is a witness to the 'victim' falling as a result of the push and being left unconscious....
The CPS, when considering a case, asks two questions;
1. Is there enough evidence to bring a sucessful conviction.
2. Is it in the interest of the general public to bring this case to court and try to secure a conviction.
This case comes down to two things, your son's word against the lad's. Your son has one credible witness, whereas the Police has none, not even the victim -
so, from my studies of the law, I would say that this case will never go to trial, in short there is nothing to worry about.
However, if it does, I would suggest taking the legal advice and paying the fee for the soilictor.
Unfortunalty, I don't think you can get the fees back from the police either 1.) without a long process or 2.) at all.
All the best anyway though, hopefully I've been some form of help.
Marcus