Hi Eddie,
"Does it make a difference that the cut head was incidental to the push ? In that the push caused the cyclist to fall down the embankment and as a result cut his head "
The unlawful push caused to cyclist to fall then sustained the 'indirect' injury.
ABH = Assault Occasioning actual bodily harm. Occasioning: means to cause, and there must be both factual and legal causation. The Defendant’s conduct must cause the ABH. In relation to causation in law there must be a culpable act that must be substantial and operative and there must be an unbroken chain. No need to show accused intended or was reckless to causing ABH.
However, the mens rea for Sec 20 wounding (not GBH) is maliciously. It was confirmed by the House of Lords in Savage; Parmenter that the Defendant acts maliciously if he intends his actions to CAUSE SOME HARM to another or is subjectively reckless that his actions might cause some harm. Not necessary for the Defendant to foresee a wound or GBH. Proof that the Defendant foresaw some harm might occur as opposed to would occur suffices: DPP v. DA.
Here is the case law DPP v Parmenter [1991]. (See how the Sec 20 got knocked down to ABH).
The defendant had caused injury to his young baby by tossing him about in a way which would have been acceptable with an older child, but not with one so young. He did not realise that he might cause harm by this action. The House of Lords held that he could not be liable under s20 as he had not foreseen the risk of any harm. It was not necessary under s20 that he foresee the grievous bodily harm which must be caused, but the defendant must foresee that he might cause some harm. An alternative verdict under s47 was substituted.
This is a basic explanation as there is tons and tons of case law on this subject.