Rain days happened even when I was at school, but we called it wet break or something similar. I can't remember how much rain triggered wet break, but it definitely had to be more than drizzle.
What happened yesterday was it had been raining, the playground was wet and therefore could be slippery - and it's on quite a slope - he was playing a game of tag, which obviously involves running, and he was nabbed by one of the "PTAs" (I think they're actually called SLAs), told no running when it's wet and made to stand on the naughty wall for five minutes (standard punishment). Then at the end of break all the naughty wall standers have to go to the office and explain themselves, apparently he was told "no punishment for that". So it all sounds like a case of an overzealous SLA - but of course I only have his word for this, there might well be more to it. He was still very upset about it at the end of school though.
Running is not generally forbidden, the kids do play tag, football and even British Bulldog although that is banned due to (I think) smaller kids getting knocked over. Top Trumps are also banned! Either because the cards were getting lost or they were causing fights - or perhaps it was causing fights when kid A loses kid B's cards.