I've enjoyed the occasional naked swim in the sea and in lakes. I like running barefoot too, and I think I might enjoy a naked run if there weren't such a strong social taboo. (There are taboos about skinny dipping and barefoot running too, but I don't think they're as strong).
The main reason people have given in this thread that such things are unacceptable is that public nudity, especially male nudity, can cause fear and distress, but as I suggested in a previous post, public dog walking can also cause fear and distress, and nobody is suggesting that that should be unacceptable or should be confined to designated areas. Responsible dog walkers can reduce (but not eliminate) the risk of causing fear, distress or physical harm, and I think naturist walkers and runners can too, for example by avoiding crowded areas, keeping their distance as much as possible, and covering up if they see any signs that they're making people uncomfortable.
One objection which has been raised is that some people may find wrinkly naked bodies ugly, but I don't know whether anyone would seriously defend that aesthetic argument.
Another objection is that public nudity goes against social norms and mores in this country. This is an appeal to tradition, and I think it begs the question: it's like saying this is unacceptable because it not accepted.
Some posters have insisted that any man who walks or runs naked outside of designated areas can't be a naturist because no true Scotsman naturist would do that. And if he's not a naturist, he must be an exhibitionist, a 'pervy flasher', who gets thrills by forcing unwitting and unconsenting passers-by to look at his genitals.
I hope the OP's worries have not been aggravated by some of the more extreme comments on the thread, and possibly she may have been somewhat reassured by the news that this man has now presented himself to the police, though she may not be happy that he intends to continue his naked runs.