This is what Andi has said -
have traced Zachariah on Ancesty (a family tree website that I subscribe to), which has really good records for London births, deaths and marriages, which I have cross-checked with Census data to verify a lot of the family connections for people alive after 1841.
Not sure if you know, but there is also a free website set up by the Mormons which contains church records (baptism, marriage, death). I don't know the www. address - I always look up Latter Day Saints in Google to find it.
From these I have traced Zachariah's line back to the mid 1700's in London. His grandfather John married Mary Lambourne in London in 1752 and his father John married Ruth Valentine in 1787. They were all married in Churches, so I'm not too sure about any Jewish connections.
The Jemima probably came from Jemima Jones who was Zachariah's daughter in law. She was born in Salisbury, but with the name Jones I can't get further back than her parents!