Which of those are you imagining doesn't have horse chestnut trees? (Conkers come from those, not plain chestnut trees)

I'm sure there are parts of the country where they're less common, but there's huge numbers of conkers falling off trees in big British cities (even if the majority will be in parks) as well as in the countryside. We played with them at my pre-teen city centre school for sure, and the trees are a common sight on roads and in gardens as well as public parks.

edit: the Woodland trust actually says "Though rarely found in woodland, it is a common sight in parks, gardens, streets and on village greens."

Live in London in Zone 2 and there are absolutely tons of conker trees around me including in areas which are not posh. They are very common in an urban setting.[1]

[1] Which kind of sucks for me personally because they cause me really terrible hayfever. I think I'm specifically alergic to their pollen maybe.