You "May" be able to claim from the pedestrian, but don't hold your breath as many car/pedestrian claims in recent years have gone in favour of the pedestrian for a whole number of reasons.
Firstly, be careful of using a claims management or investigation company (I will say no more than that, just be careful).
If it were to go to trial, the Judge will look at the circumstances, in particular the location. If it is an area that is a high pedestrian density area then there is a big chance that the claim will fail or you will be hit with a large degree of contributory negligence. Why?
What the judged have been saying is that if it is in a high pedestrian population area, then you as the driver should be aware of the potential for a pedestrian to do something stupid and therefore drive with that anticipation in mind.
Even though it is the pedestrian that caused the impact, you as the driver are often held liable.
If it happened in a more rural or less populated area, then you may have a bit more success, but this has been countered in recent months by the additional rules in the Highway Code regarding pedestrians, and so a degree of contributory negligence might be levelled at the driver.
Was the pedestrian injured?
Is there a claim coming your way for injuries sustained by them? Statute of limitation is 3 years for personal injury. Don't be surprised.
A few years ago I investigated a car v pedestrian crash. The pedestrian was drunk, stepped out into the road int the path of the approaching vehicle and was badly injured.
Liability went fully in favour of the pedestrian on the grounds that I said. It was a high pedestrian density area, late at night with the possibility of drunk people randomly walking into the carriageway. It was held that the driver should have anticipated that possibility and driven accordingly (His words not mine)
In another a drunk was lying unconscious in the road because of drink, again got hit and liability went in the drunks favour for the same reasons.
Even if you were successful against the pedestrian, do they have sufficient insurance cover through house contents insurance or other policies that would cover any liability and legal costs? Probably not.
So if a judge were to make a n award in your favour, chances are you would get drip fed at (for example) £1 a month as being all they can afford.
If you put it in the hands of solicitors, the claim has to be worth £5,000 or more before that can start claiming legal costs back, so it would result in you having to issue proceedings yourself.
So good luck, but don't hold your breath.