Lower Mill？

It's a place name. We have an Uppermill near here.

A private nature reserve is just an area which is well-wooded and is closed to the general public. A private park could be so called, if wildlife were plentiful there.
It is probably NOT stocked with exotic species, just native species occurring and reproducing naturally.

The dirty buggers.

Don't confuse the foreigners.
And, it can be beautiful.

It was flying ant day on Monday. I did not find the copulating ants on my windscreen at all beautiful.

http://www.holidaylettings.co.uk/lower-mill/hom_home_type.cottage/