I better put this here first ( although I found it after doing all the research below.....:-))
I found a few things that may interest you....Cornelius was a witness in a murder inquest in 1870:http://trove.nla.gov.au/ndp/del/article/5838298?searchTerm=c...
from a quick read ( its long article ), it seems Cornelius used an alias of NEAL or NEIL - you will find the article quite amazing for its detail - if not for the shock it will give you!
I also found in 1796, a James and Cornelius CHIDGEY were bricklayers living Marmaduke St London - they became bankrupts.
I also found your Cornelius in the censuses, living with his parents, Cornelius, bricklayer b 1815 and Sarah..along with siblings. I found your Tree on Ancestry and didn't find your Cornelius' parents, so thought you might like to know all that info is available.
Chidgey passenger arrival 1897:http://trove.nla.gov.au/ndp/del/article/69901666?searchTerm=...
plus you can see your early family getting the ' Freedom of the City"....I can email this directly if you are interested:
London, England, Freedom of the City Admission Papers, 1681-1925 about Cornelius Chidgey
Name: Cornelius Chidgey
Residence County: Middlesex
Admission Date: 5 May 1795
Master's Name: William Chidgey - a citizen and cooper
Father's Name: James Chidgey - bricklayer in the parish of St George in the East
James was b 1781 and was the son of Cornelius and Christiana, nee DOWSETT who married 01 May 1780 - both could sign their names
You will also find an article about Saul FLATAU's father Will - they were Jewish:
The Argus (Melbourne, Vic. :Friday 6 November 1896
That Cornelius was b 1756 and died 1824
actually there is quite a bit in the papers fr the FLATAU family
going back to NZ...I found a marriagae for a Lydia to a Charles COX in 1882 -But I think its the sister to your manhttps://www.bdmhistoricalrecords.dia.govt.nz/search/
these are their children - looking very promising
1885/19559 Cox Ruby Henrietta Lydia Charles Henry
1883/8242 Cox Eleanor Lydia Charles Henry
1889/14003 Cox Effie Cora Lydia Charles Henry
1894/16783 Cox Douglas Cornelius Lydia Charles Henry
1898/12329 Cox Marjorie Fiona Lydia Charles Henry
1906/3704Eleanor Cox William Joseph Robinson
1913/8679Effie Cora Cox James Winchmore McLean
1916/955 Zoe Marie Armstrong Douglas Cornelius Cox
1928/8880Marjorie Fiona Cox Cecil John Christian
1951/35591 Cox Ruby Henrietta 65Y
1962/33598 Cox Douglas Cornelius 67Y
I'll send this off and keep looking for Lydia Henrietta - and Cornelius, alias NEAL/NEIL!