From the Wikipedia page 
During the nineteenth century large areas of the forest began to be inclosed by private landowners, leading to the loss of commoners' rights and of public access. An act of parliament, The Epping Forest Act 1878, brought an end to this and ensured that the forest remain a public amenity. The act appointed the City of London as the Conservator of Epping Forest.
The forest has been designated as a Site of Special Scientific Interest (SSSI).