Tree in the Wood is the most common published title and one I tend to use most. Definitely PD. I can take the date back much earlier than 1877. A version appeared on a broadside c1800 (song 1 of 2 Excellent New Songs) printed in London, ref British Library 11606 aa.24 (7) 1 The Tree on the Hill (probably much earlier). The Pitts broadside referred to by Mick can be dated c1800 to 1819. Randall of Stirling printed a version 'A New Song Called Oral Valley' in 1805 which can be seen on the National Library of Scotland site. There are later printings as well by Pearson of Manchester. There is enough difference amongst these versions to suggest they derive from something earlier.

BTW 'New' means nothing in such cases. It was simply a sales ploy.