There's a family which may be of interest, though details are not perfectly matched.
Harriet Smale and various children of hers spent time in the Strand and Edmonton workhouses in 1888, and she and the youngest child Alfred spent time in the Islington workhouse in 1890.
Children (from workhouse records):
Harriet b 1876-7 - born 3 Nov 1876 and baptised as Harriet Emily Smale, 14 Jan 1877
Henry b 1878-9
Elizabeth b 1879-80 - Elizabeth Smale, mmn Wilson, Mar qtr 1881 St Giles
Ann b 1883-4 - Ann Smale, mmn Wilson, Sep qtr 1883 St Giles
Alfred b 1885-6 - Alfred Smale, mmn Wilson, Dec qtr 1885 Strand
Harriet snr may be the Harriet Wilson who married Henry Smale, Mar qtr 1876 Bethnal Green.