The IOPC doesnt discipline anyone, but where the investigation leads them to it they will refer the case to the police force or in criminal matters the Crown Prosecution Service who would then assess whether a conviction would be viable based on the case that can be presented in court. You can scroll through their news feed and see instances of convictions being secured fairly regularly.

Also important to point out that it is illegal for police to unionise. Instead they have their own counterpart to the IOPC, the Police Federation, who are also government funded and provide independent advice and representation in worker relations and disciplinary hearings, but without the politics. Also that the CPS is a professional organisation - prosecutors aren’t elected. So the general theme is to try to uphold the law and professional standards rather than to score points in the media.

From a barebones perspective, unless the officer was waving the gun around indiscriminately, and as long as their blood test comes back clean, it’s likely to find that the perpetrator was a) clearly homicidal, b) non-compliant, and c) wearing a bomb vest (that it was fake is immaterial), and that the synagogue was filled with his intended victims, and that the officer was therefore likely correct to end the threat to life despite the possibility of collateral damage - it’s a higher acceptable risk in this sort of situation as the potential deaths from bombing are devastating.

A lot will go into how accurate the weapon is, and whether the officer was up to marksmanship standards, and to the choices of the force in terms of training, equipment and tactics. The officers involved will have to account for each decision to pull the trigger. Every bullet accounted for in intent.

Ultimately as he was wearing a (fake) bomb vest it was clear the perpetrator intended to kill until being killed, and so their shooting will almost certainly be justified by the investigation. What’s in question is the other death and the injured person.

The system is not perfect at all and police abuses do happen - the BBC just broke a story about systematic racism in the Met - but deaths following police interaction are extremely rare therefore always national news and high profile, and the British principle of “policing by consent” binds the powers that be to support an independent process rather than “backing the boys in blue” like you hear from American politicians. That’s why the police have been so quick to publicly acknowledge the possibility the bystander was shot by police.

I can’t think of any similar situation where a bystander was shot since Jean Charles de Menezes in 2005 (though that was an intentional but mistaken killing), and that still provokes outrage over the police lies.

EDIT having reviewed the reportage

It seems to be the case that the two bystanders who were shot by police were leaning against the synagogue door on the inside and that when the perpetrator was shot, rounds passed through the door and hit them. Under such circumstances it would seem to be the case that this was a tragic outcome, but that the firearms officers couldn’t possibly have accounted for it in their actions, given the stakes of a presumed suicide bomber trying to gain entry. A horrible event all round, but it would be hard to claim negligence by police. If there is an outcome of the investigation it may result in recommendations about the power of firearms in use but that would then risk being unable to stop a threat when it counts. Tragic, but seems genuinely not an example of police being the problem.