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Those are usually the former carriage-roads, i.e. (often) circular routes along which the gentry could drive their horse-drawn carriages on Sundays after church, and they very much pre-date mass motorisation. I imagine that when people first took to motorised carriages, these roads would have been used in much the same way for a while before they became through routes. They certainly need to be barred to through motor traffic, but there's very little chance politically that this is going to happen in South-West London any time soon. London certainly should have kept the roads restricted to leisure traffic only (although, without any doubt, many bike riders in Richmond Park go too fast to deserve that label), but people basically didn't know how this mass-motorisation lark would turn out. :)
My point was less about the speed of cars, more the volume and the propensity in London to stick big roads through the middle of parks.