Loads of chestnut trees in Poland too - they're actually the national tree of next door Ukraine and originated in the Bulgaria/Greece region - but no conker games either. Instead, Polish kids make little figures out of them with matchsticks for arms and legs.
Has the chestnut-destroying beetle - I can't remember its proper name, but it also comes from Greece and is spreading northwards - reached the UK? It breeds in piles of leaves on the ground over winter.