No not everywhere, but as the parent comment is talking about the Britain, the natural state of the UK before human intervention was a heavily (perhaps not densely - I don't know) forested island
That's not really the case. It was a widely held belief or myth that the British isles were covered in dense forest. The coverage was at most about 60% and also that humans have always been intervening in the landscape and they arrived very soon after the glaciers retreated up north. Most of the woodlands were managed or occupied and there were not many places which didn't see the human touch (in Britain) compared with other places in the world.
In part the myth of the virgin untouched forest comes from colonial views of natives existing in harmony or as part of nature and not really human. Even in the US, Native Americans have been managing the "wilderness" for thousands of years before the US Forest Service.
Not sure about the environment of the British Isles, but that of North America is not and was not a monolith. Sure natives in some areas were burning some vegetation, but that didn't happen everywhere. Actually in some areas the burning was only of undergrowth, so that it actually made the canopy more dense than it would have been without burning.
In part the myth of the virgin untouched forest comes from colonial views of natives existing in harmony or as part of nature and not really human. Even in the US, Native Americans have been managing the "wilderness" for thousands of years before the US Forest Service.