It seems the festival died out (sadly) early in the 20th century. Small parts of Hainault Forest remain and it's a lovely place for walks. There's very little happening in the way of traditional music, song, dancing, etc. in the general area.
A young oak tree was planted to commemorate the great Fairlop Oak at Fullwell Cross.More information if you're interested:
http://www.hainaultforest.co.uk/3Fairlop%20Fair.htm
http://www.british-history.ac.uk/report.aspx?compid=42724
Garry