This is a really interesting question. It's probably not really advertised because the potential impact of injury is so insignificant than say for driving where third party insurance is mandatory. It's also hard to identify someone compared to a car reg.

Suing for injuries in the UK is actually pretty difficult and you have to show real harm / loss of earnings etc. In a lot of cases that do happen with car insurance is that the insurance company find it quicker and easier to settle than to fight, as the costs just get eaten up by the cost of insurance for everyone going up. You would have a much stronger incentive to defend and challenge any claims made personally against you.

There are a few cases of cyclists being sued but seems to usually be when they are cycling on a pavement or aggressively, although this case the fault is not as clear: (https://www.theguardian.com/law/2020/feb/24/cyclist-settles-for-30000-pounds-after-hitting-pedestrian-who-was-looking-at-phone). Even this is an extremely rare situation that it got national news attention and cyclists chipped in to help them pay the settlement. I'm a member of a cycle club that includes free third party insurance that the otger poster mentions.

I can't find any details of where a pedestrian was sued for hitting another pedestrian other than people pushing others in front of a bus / train etc.

If you were sued, the biggest cost would be the legal cover which could be covered by home insurance but is often an add-on - I've always added it on or gotten a policy to include it, which I think is enough to cover anything.

Just out of curiosity, why are you looking for this cover?