More rural areas yes, but England has been shaped by human activities for a very long time. Rural areas are not more "natural" (as in free from human influence) than cities.
Yes, we have very little left of the primary forest that predated human colonisation over much of the British Isles. Areas that we now perceive as wild countryside are usually anything but. One example is those moorland uplands which (in Scotland) were the result of enforced clearances [0] between 1750 and 1850 and which are now often optimised for grouse shooting. The New Forest, my closest national park, is essentially William the Conqueror's hunting estate and where land use and ownership been very tightly controlled since then.
Thus, any notion of a truly natural landscape of forest in the British Isles disappeared since long, long before the immediately pre-industrial era. Likewise applies for much of Europe even. Again, an example: the landscapes of modern Spain, France and Italy, were repeatedly cleared of forests during their history, particularly by the Roman Empire's needs.
Of course, on the other hand, you could also define natural to mean anything allowed to grow without human intervention for X number of centuries, in which case, yes, there have been many truly natural old growth forests in Europe well after Roman times, simply because they regrew during the hundreds of years between the fifth century and later, heavy population growth prior to the disastrous 14th century depopulation stemming from the Black Death and Great European Famine of the early 1300s (thought to have possibly been caused by a massive volcanic eruption somewhere else in the world)
Anthropic reach extended since then (e.g. compounds tiny enough to get in blood, or scale of activity creating global impact), but when it comes to landscape, we have been the shaping factor for a very long time.
[1]: https://www.researchgate.net/publication/236630316_Open_wood...
Edit: The more I think of it the stone construction really is the most unnatural part. Especially the ancient tradition of building those little walls using the stones you cleared in order to plow.