"Natural" woodlands are managed by suites of herbivores, whose diverse feeding methods have different impacts on vegetation. Those herbivores are in turn managed by predators stalking the herds, causing them to shift about over time and thus creating a mosaic of habitats in different successional stages.
Management by humans is necessary only because those herbivores and predators are mostly extinct in Europe.
For this reason there is no unmanaged-but-natural woodlands in West Europe. Białowieża in Poland is probably the closest example - and it's awesome
https://en.m.wikipedia.org/wiki/Bia%C5% ... BCa_Forest
The UK does have plenty of spare space. Deer-shooting estates in Scotland alone add up to an area larger than Yellowstone, so there's no reason we couldn't have woodlands full of bison and wolves - except for the issue of ownership.
So more practical models generally involve using a range of farm animals to do the grazing/browsing, and people to do the predation. It's still way less work than manually coppicing everything, and sites like Knepp in Sussex and Oostvaardersplassen in the Netherlands show that natural ecosystems can be restored quickly, easily and cheaply once you have the land. Loads of marginal farmland will be going broke without EU subsidies, so there's an opportunity to do something useful with it.
As for what they're for, the obvious answers are things like carbon sequestration and biodiversity. The UK has committed to 68% carbon reduction under the Paris Agreement and to protecting 30% of its land for nature by 2030, targets that will require a lot of hard work to meet. I'm sure the UK wouldn't want to renege on international commitments.
Native woodland is much better than monoculture plantations at both of those things, especially compared to the conifers preferred by commercial forestry.
In terms of human access, all 3 sites mentioned above are highly popular wildlife tourism destinations. Generally these things operate with a core area people don't visit much, and a buffer area where they do. Wildlife from those forests would also spillover into the rest of the countryside - loads of common bird and butterfly species are declining very fast in the UK. If people want to keep seeing things in their gardens and on daily walks, they need big areas of proper habitat to deliver their nature.
We have the right to a clean, healthy, sustainable environment.