A quick google will get you websites of primary schools up and down this great nation with photos of their Conkers champions holding up their trophies.
As for "the law" - from a 2019 petition to make conkers legal again:
There's no law or government policy banning children from playing conkers, so we're not sure exactly what you'd like the Government or Parliament to do.
As for "the law" - from a 2019 petition to make conkers legal again:
There's no law or government policy banning children from playing conkers, so we're not sure exactly what you'd like the Government or Parliament to do.
https://petition.parliament.uk/archived/petitions/238105