The Chase Dagenham Walk
This National Trust owned nature reserve has 143 acres of woodland to explore on a number of footpaths. It is located near to the villages of Woolton Hill and Enborne Row on the Hampshire/Berkshire border. The area consists of broadleaf and coniferous woodland with streams and lots of interesting flora and fauna to look out for. The snowdrops in early spring are particularly lovely. There is a car park just off station road which gives direct access to the trails.
It's easy to extend your walking in the area by heading into the adjacent Penwood forest. You can also visit the real Downton Abbey at Highclere Castle just to the south of the reserve. Walbury Hill and Pilot Hill, the highest points in Berkshire and Hampshire respectivley, are also close by.