This Margaret is one to look at but not really much to go on.
Firstly, she is born Salford not Manchester 
I think this is the right birth
Margaret Mary Taylor September quarter 1886 mmn Riley
1891 3218 /134
Long Street, Salford
Joseph Taylor 41 yrs ?plate worker b Ulverston
Margaret Taylor 38 yrs b Whitehaven
Oliver Taylor 13 yrs
M Ann Taylor 4 yrs
Jos Ed Taylor 2 months
Children b Salford
1901 3726 /10/11
Walnut Street, Broughton
Birth registration for Oliver Taylor in 1878.
Mother's maiden surname RILEY. GRO Reference 1878 M Quarter Salford Volume 08D Page 73
Lancashire BMD births index has an entry for Olive TAYLOR in 1878 in Broughton sub district. Lancashire BMD is compiled from original certificates.
Marriage in Lancashire BMD marriages index:
TAYLOR Joseph
RILEY Margaret
1877 Salford Saint Simon
St. Simon C. of E., Springfield Lane, Broughton
www.lan-opc.org.uk/Salford/Broughton/index.html