I think that Daniel Carey was somewhat older than he admitted to - he states born Whitechapel on the census and there was only one: bc.1856, son of Thomas and Julia. From 1861 census Julia's mother is living with family i.e. Catherine Sullivan.
I can now add 2 further spellings to the mix - looking for a marriage Thomas Carey and Julia Sullivan brought up zilch so searched under her name and eventually found:
Thomas Geary, son of Thomas married Julia Sullivan, dau. of Timothy, on 24/7/1853 St. Thomas, Stepney.
Looked for son Daniel's birth but cannot find a likely entry but I did find his baptism:
Daniel Gary b.7/6/1855, bp.17/6/1855, St. Anne R.C. Church, Underwood Road, Middx (London).
Cannot find a marriage between Daniel Carey/variants to Eliza Martin. With regards to the latter, think she was the daughter of Thomas Martin and Eliza Beeten who married in 1858 Mile End. 1861 and 1871 census state she was born Poplar but in 1871 they are living in Shadwell.
Annette