The Crown Prosecution Service's website makes the guidance that's primarily intended for use by its own staff available to the general public. While such guidance isn't, in itself, a statement of the law, it's based upon rulings made across many courts over several decades. So it's always a useful starting point when seeking to answer questions like this.
Based upon what I read there, my best guess would be a 'Section 20' GBH charge:
https://www.cps.gov.uk/legal-guidance/offences-against-person-incorporating-charging-standard
(An earlier version of the CPS website provided a list of the types of offences which would fall into 'ABH' or 'GBH'. If my memory is correct, that list included a fractured jaw within the list of 'GBH' injuries).
The Sentencing Council also makes its guidance for magistrates and judges available to the general public. See here for the guidance relating to 'Section 20' offences:
https://www.sentencingcouncil.org.uk/offences/crown-court/item/inflicting-grievous-bodily-harm-unlawful-wounding-racially-or-religiously-aggravated-gbh-unlawful-wounding/
As I see it . . .
Culpability = C
Harm = 3
That leads to a 'starting point' sentence of 26 weeks custody but with a sentencing range of between a 'medium level' community order and one year's custody.
My guess is either that a custodial sentence could be avoided altogether or, alternatively, that any custodial sentence would be a suspended one. If, Dampbunny1, you're 'Person B' is this scenario, I think it highly unlikely that you'd receive an immediate prison sentence.
[Disclaimer: New Judge is, as his name suggests, a judge. I'm just a guy who takes an interest in the law. So his answers should take precedence over mine. However I've used authoritative sources for my reply, so I hope that my post is still of some value here].