Don't hold your breath!
Would you like a "sympathetic police force" to ignore half of the facts in a case in order to pursue a particular agenda?
By the way, I've kept quiet on this thread to date, not least because I think that under the circumstances the fact that the driver got a caution was well in keeping with what normally happens, according to very strict guidelines set by the Home Office and applied strictly by Evidential Review Officers and the CPS. First offence, no serious injuries from the actual assault (we'll come back to the elbow later) and a caution is in keeping with what was to be expected.
The OP has made a formal complaint because it took 5 weeks to progress to that point. Really?
Now that we have a second perspective thanks to GC's persistent questioning and Boris's more direct approach, we have the suggestion (and some evidence) that the cyclist slapped the van. Still no excuse for what happens next, the assault is absolutely unforgivable, and the assailant now has a record for his actions. However, I can be in no doubt that the driver will have been interviewed and will have advanced the mitigating factor that he was annoyed at having his van slapped.
Faced with this the officers will have been duty bound to make further enquiries around that assertion, and this will have prolonged the decision making process. We don't know (and I doubt if we will ever find out) exactly what that decision making process is or was, but given what we now suspect, a caution for the punch is quite a result.
We also don't know whether the incident was dealt with as a Road Traffic Collision. I suspect that the driver has told the police from the outset that he didn't hit the cyclist, but that the cyclist slapped his van. This is why the police didn't issue a Notice Of Intended Prosecution as sue tells us higher up thread.... because as far as they are concerned no offence has been committed. To confuse matters however, there is no legal need to issue an NIP if the offence in question involves a collision of which the driver is aware.... so legal moot point on that one. Did the police consider the matter to be an RTC? Indeed, did the OP ever report it as such or did he just tell the 101 operator that he had been assaulted?
Either way, sue has posted the incident and invited us to think of the police who dealt with this as lazy, incompetent and unsympathetic. There is a suggestion he has been caught out in a lie, and is even prepared to pervert the course of justice, and I note that he has plenty of time to respond to these accusations, but so far hasn't. As a committed professional whose job is to address and improve public confidence and satisfaction in the service I represent this makes my blood boil. There are enough examples of police idiocy and incompetence for real without someone making stuff up to discredit us FFS.
What's even worse is that he has claimed that the incident has cost him five weeks off work and intends to pursue the matter civilly. Glasgowcyclist has echoed many sentiments here inasmuch as we hope he isn't tempted to make things even worse by being investigated for criminal deception.#
Oh, and a big shout out to
@Mugshot 's tenacious detective work and keen observation. Not to mention veloevol's HD slomo.