I've often wondered about this - it probably boils down to some ancient law dating back to the Magna Carta or earlier - isn't it called 'estovers' or something? Anyway, I guess that in order to qualify for the right to collect firewood, you have to be a bona fide peasant or something, so best of luck!
We have no occasion for firewood in England, but we do in France, where it's even more of an issue, seeing as, in rural France anyway, everyone burns wood (it's the cheapest form of fuel for house heating, even if you're forced to buy it), and there's always plenty lying around. And indeed you often pass folks stopped by the roadside in their little Renault vans busy sawing away. We've had neighbours tipping us off about a fallen tree near the village, and it's first one to get there gets lucky, sort of thing, but we prefer not to be greedy. At present we don't visit in the winter, and there's plenty of prunings from our own garden to warm the house in the spring...