No, not yet Merry.
My current theory is:
Births Dec 1861
BROWN John Edwin Clifton 6a 135
Deaths Mar 1863
BROWN John Edward Clifton 6a 107
...are the same child, James' son with his first wife. The details for these on FamilySearch list James and Elizabeth Brown as the parents. He later had a son by the same name with his second wife, who is:
Births Jun 1867
Brown John Edward Clifton 6a 153
I have a scan of John Edward's birth certificate sent by a relative. His parents were James and James' second wife, Emma Elizabeth Cowley.
James' marriage certificate to Emma (April 22nd 1866) does list him as a widower (and mason) and her as a spinster. The father's name is given as William Brown, but we can be fairly sure he was a bastard.
Between 1863 (the first John Edward's death) and 1867 (the year after James re-married) there are four deaths for an Elizabeth Brown in the Clifton district:
Deaths Mar 1863
BROWN Elizabeth Clifton 6a 121
Deaths Jun 1863
Brown Elizabeth Clifton 6a 93
Deaths Mar 1864
BROWN Elizabeth Bonbonous Clifton 6a 66
Deaths Dec 1865
Brown Elizabeth Clifton 6a 61
This is of course assuming that Elizabeth was her real / first name, and she died in the Clifton area.
However, chances are that one of these is James' first wife.