I live in UK and it seems that for most pedestrians and cyclists road signs are just a decoration. I often had pedestrians dash through red lights, even if I have engaged the crossing. Being on a motorbike, it wouldn't take much to tip me over if a pedestrian were to run into me. If that happened, who would pay for the damage, since pedestrians don't have insurance?
Some pedestrians do have insurance, of course, but we can assume that the one in your hypothetical did not. Before we think about insurance, though, we need to think about liability. We don't need to think about it too much, though, since it seems to be one of the assumptions of the hypothetical that the pedestrian is fully liable.
In that case, the pedestrian's liability insurance, if any, might cover (some of) the pedestrian's liabilities. To the extent that the insurance does not cover them, or if it does not exist, the pedestrian will be, well, liable for the rest.
To the extent that the pedestrian cannot afford to cover the (remaining) liability, your insurance may do so, if it includes coverage for losses that you've incurred but cannot collect from the liable party.
If there remains any uncovered amount, you will have to pay that out of pocket.