What a storm in a teacup this thread has been! I can understand why the OP might be so concerned, but as mentioned many times, it's highly unlikely that they'll hear any more about the incident from the police, no matter how much other members here would like. The poster above used the phrase "trouble knocking on your door". By obsessing about it so much, you're only getting closer to knocking on trouble's door. The police have protocols and procedures they had to follow and I doubt they were anything to do with the fact that you were riding an electric bike, illegal or not. I'd wager they'd have done the same had you been riding a 'hobby horse' down the road.
I agree with you, it's extremely unlikely that the police will investigate any further unless the alleged injured person pushes very hard for them to do so, which I doubt will happen.
If the bike had been fully compliant with the law, I think the OP might have had a degree of cover from their home insurance. I know that every policy I've had has covered me for any harm injury or loss caused to a third party as a result of my actions at or away from home (with certain exclusions, the main one being use of a motor vehicle).
If a serious injury had been caused in the circumstances the OP describes, then I think it would be a different matter. Especially if a child was hit and injured. The police would almost certainly be interested in the bike, more so if it was disclosed that a motor was fitted to it. Potentially, this could lead to a whole heap of trouble and personal expense.
I don't think you would be entitled to free legal advice. I'm pretty sure that it doesn't extend to the Road Traffic Act and any personal liability insurance held would be invalid. You would be required to fund everything.
Riding an illegal bike leaves the cyclist exposed to potentially ruinous expense and costs if they hit a pedestrian. We know that bikes do collide with pedestrians and we know that these collisions have caused deaths and life changing injuries. That's a fact. By the laws of probability, one day an illegal ebike will hit a pedestrian with the same outcome. It has to happen and the odds shorten each time a new one takes to the road. Potentially being ruined financially is not something I want to expose myself or my family to. It's not worth it for an extra 10 mph, or less.