Don't know if this ties in with your information but there's a Wren family in Luton in 1871 census
Thomas WREN - age 20, born Herts Ware, Fish Monger
Emma Wren - age 22
Emma Wren - 5 months
1872: Death, registered in Luton (March quarter) of Emma Wren, age 23
From Hertfordshire Advertiser dated 23 March 1878:
DEATHS:
18 March 1878, at Hertford, Mr Thomas Wren, age 26
Oddly I can't find this death registered on Freebmd

1881 census has Emma Sophy WREN living with her Aunt & Uncle George & Caroline Jennings. She's age 11, born Ware.
There were no other registered births in Herts for an Emma Wren apart from Emma Sophia Wren - Dec Qtr 1870 (3a, 240). Logic says this is the same child.
1891 census - young Emma Wren is a servant in Hackney
She married Albert White 31 Oct 1903 at MEOT (London). Her father's name is recorded as "Ernest Thomas WREN"
Hope something here is of use
EDIT - red warning - shall post anyway just in case ...
- apologies Rosie - I've duplicate a lot of your info (slow typist

)