From the article you linked:

> The solution in Germany was a series of forts and fortifications, called limes, which used timber from the great central European forests and ditches to prevent tribal incursions. In contrast, large forests did not exist in Northern England and a great wall was built using stone...

That suggests there couldn't have been that many trees to fell in the first place. The terrain simply doesn't support it up here, about all it's good for is grazing, which is why you'll see field after field of sheep in Northumberland and not a lot else.