Very, very grateful to you Gadget for your efforts on my behalf. So it looks as though it has to be Barnet. The Enfield Lenharts had a daughter who was 19 at the time of my grandfather's supposed birth date of 1882. She could have been his mother who maybe was sent away from home to have her illegitimate child.
I think you will find Barnet in Hertfordshire , You might want to try Brent or Friern Barnet these are or were in Middx . Google Friern Barnet its near Muswell Hill, Finchley and not very far from Barnet Regards Tony