Hi Robbie,
Yes I found the same as you with regards to the baptisms and burials of John and Jane.
I have been in contact with Robert Jones (the poster on here) the connection with Martha is I think his gg or ggg grandmother was Martha's sister. I do use familysearch often, but I hadn't seen that tree on there.
I also use ancestry and found a lot of the Clarke's baptisms and marriages on there, there were quite a few William Bishop Clarke's, sons of different members of the family, my g grandad was Edward Clarke son of William (Bishop) Clarke and Ellen Parr, Edward married Catherine Hughes, one of their sons was William Bishop Clarke, but he died in infancy 1901 11 months old, he had a twin sister Ellen, who also sadly died in infancy I think she was 2 months old. Toxteth Cemetery burials are online, and I found a lot of the Clarke's buried there. William (Bishop) Clarke died October 1895 but only registered as William Clarke, I have his death cert, he died in the Southern hospital, from lockjaw, he is buried in Toxteth cem. Addresses for them are either 74 or 76 South Street Toxteth (Edwards family lived there).
Plot and grave no c1 56 (sadly no headstone)
Jan