The police are the investigating team for the prosecution (CPS/DA/ADA or the like). They have the responsibility of deciding if taking no further action in cases that cannot meet the appropriate evidential standard and without the need to refer to a prosecutor. The police also assess whether cases meet the legal threshold test on available evidence to present to the prosecution for a charge decision. So in short, if the police believe he acted lawfully, they can end an investigation.
The decision to charge and with what is a serious case is the responsibility of the prosecutor, we'll say the CPS for argument's sake. The CPS will have to consider if the evidence available is usable in court and that it is reliable and credible. The CPS will have to determine if there is a realistic prospect of conviction. The case must also be in the public interest and the CPS must consider the costs involved in bringing the case to trial (a highly debated aspect). This case is very complex and I have zero doubt that the prosecutor, not the police, would be charged with making the decision to proceed or not.
Could he be charged with murder? Yes. Murder is committed when a person of sound mind unlawfully kills another person (actus rea) and they have the intention to kill or to cause grievous bodily harm(mens rea), both mens rea and actus rea must be proven to be convicted. It could be argued that when the defendant decided to get into the car and drive it at the attacker that the defendant should have had a reasonable mind that his actions would cause death or serious harm.
Could he be charged with involuntary manslaughter? Unlikely. As above but without the intent to cause death or grievous bodily harm, this is less likely to be argued successfully as the outcome was the death of the attacker. To argue that he didn't intend to harm has little weight considering the facts known and I would advise against the charge being brought forward.
Could he be charged with gross negligence manslaughter? Unlikely. Gross negligence manslaughter is committed where the death is a result of a grossly negligent, though otherwise lawful, act or omission on the part of the defendant. It could be argued that when the defendant chose to get into the car with the intention to drive at the attacker that this was not a legal act. If the defendant ran over the attacker on the road whilst driving to the shops, the defendant may have been negligent and this charge may apply.
Could he be charged with death by dangerous driving? Yes. Causing the death of another person while driving a mechanically propelled vehicle dangerously on the road or a public place. It could be argued that the facts of the case could be applied and successfully argued.
Could he be charged with criminal negligence? Yes. Conduct where a person ignores an obvious risk or disregards the life and safety of those around him. This could be argued successfully when considering the facts we know.
It really does fall on how the investigating team (police) and the Prosecution (CPS) view the act. There will also be pressure to 'do the right thing' but what is the right thing? Believe it or not, there will be those that call for the strict law to apply without fear or favour and will want to claim justice for the attacker, both public and political pressure. For example, if the CPS decided to discontinue the family of the attacker can bring litigation in the form of a civil suit against them. There is always many this to consider.
Bare in mind, this is just conjecture and there could be different charges brought forward that are not listed above.
I hope this helps a little.
Edit: What to charge the defendant with is very important for the prosecuting team. To get a conviction they must prove the intiraty of their case beyond all reasonable doubt, the burden of prosecution.
