This has been a problem almost since they were introduced. They've just been left to get on with it, the ones at Sheringham are rather impressive though, especially when you climb the viewing tower when they are in bloom.
Back in the mid 90s my unit helped the National Trust clear a hillside. 20 squaddies and we weren't allowed to go to the pub until the hillside was cleared. It was done in a morning. The bloke from NT said it would have taken civvies over a week ;-)