I have been catching up with London and Middlesex Records and found the following:
Does the Ethel Woodley in this record match the person in your tree?
London, England, Workhouse Admission and Discharge Records, 1764-1930 Lewisham
1910 October
7th Friday D Woodley Ethel Housewife C of E 20.2.1909 She was aged 19.
There are a number of workhouse records in Lewisham for an Anna Woodley & Ethel Woodley
Anna Woodley 1870 4 Feb 1913 Lewisham, Lewisham
Anna Woodley 1870 24 Feb 1913
Ethel Woodley 1909 4 May 1911
Ethel Woodley 1909 4 Feb 1913
Ethel Woodley 1909 24 Feb 1913
Anna Woodley 1871 28 Nov 1912 Lewisham, Lewisham
Ethel Woodley 1909 17 Jan 1912 Lewisham, Lewisham
Ethel Woodley 1909 3 Jun 1912 Lewisham, Lewisham
Ethel Woodley 1909 28 Nov 1912 Lewisham, Lewisham
I haven’t looked at all these records
Im guessing that perhaps Anna Woodley gave birth to Ethel in workhouse
This appears to be her birth entrymothers maiden name is blank so assume illegitimate
WOODLEY, ETHEL - 
1909 M Quarter in LEWISHAM Volume 01D Page 1144
Possible death for Anna
Anna Woodley Death Age: 72
Registration Date: Mar 1943 Registration district: Lewisham