You mentioned public trees on Anc*y which I have just come across one names Emma's parents as
Samuel Aldred & Sarah ?no further details on parents, her Bpt 6 Mar 1828, arrival Australia 1849, 1850 marriage to Horace Bastings , names 9 children and her 1927 death NZ
I did come across a baptism for an
Emma Aldred with parents
Samuel & Sarah that was in
1833 
posting details just in case it might be relevant and you want to investigate further
Emma Aldred born
20 Sept.Baptism 27 Oct
1833 St Mary Magdalene, Woolwich, Greenwich
Father:
Samuel Aldred,
cordwainer Mother: Sarah, abode George Street
Also these baptisms, same parents, same abode
Samuel Aldred born 2 July Baptism 2 Aug 1835
Mary Jane Aldred born 26 Aug Baptism 8 Oct 1837
Another tree has
Robert & Anne Goldspink as Emma's parents she died 1927 NZ ,
Robert was a widower when he married Ann Goldspink on 13 Jan 1822, 1851 census listed,
names their children and various other info.....here's a few details
baptism at St Giles Camberwell of Eliza parents of Richard, victualler & Ann abode Peckham
on 6th July 1838
These marriage entries
Jemima Aldred f/a St James’ Terrace father
Robert, occ Maltster
16 Aug 1853 St James, Paddington, Westminster
Spouse: John Macdonell
One witness
Sarah AldredJane Aldrad father
Robert, labourer
3 Nov 1856 St James, Paddington, Westminster
Spouse Charles Sheppard
One witness
Eliza AldradIf you don't have access and want further details please come back and let me know