Well there are three Water Peppers, and none of them are that exciting. There is Water-pepper (Persicaria hydropiper) then there is Tasteless Water-pepper (Persicaria mitis) and also Least Water-pepper (Percicaria minor). There are also other species in the Presicaria genus such as the Bistorts, Redleg and one called Pale Persicaria.
The three called Water-peppers are all quite similar, with as you would expect Least Water-pepper being the smallest, and the Tasteless one not tasting peppery! Though I would not recommend tasting them as I have read that Water-pepper can cause burns to your skin so it might have quite painful effects on your tongue.
Below is a photo of a Water-pepper.
However I would not stake my life on which particular species. This is because the flowers look slightly pink. According to some text books Water -pepper has white flowers, but others say they can be slightly pink. The other two species have pink to slightly red flowers.. Hmm where does slightly pink become pink and when does that become red? That is why all bets are off. The flowers form a drooping spike as you can see and they can be found from June through to the end of September.
I have found Water-pepper mostly along footpaths, wet muddy woodland paths, It is not the sort of plant you instantly stop and admire, it is low growing and straggly, you can see I am not a fan.
So one more photos to finish off with, I think this is Persicaria hydropiper but as I said …no bets