My 2nd great grandmother, Mary Elizabeth ("Mary"), was born to Richard and Penelope Hill in Islington, London, on 01 Jan 1857. She is found with Richard, her stepmother Annie, and brother Richard D in Islington in the 1861 census, and in Hackney in 1871 with Richard, Annie, and Mary Rogers, widow of Demetrius.
In 1878 she married Herbert E Richardson, and in 1879 their son Herbert W was born. The three are in Camberwell in the 1881 census. In 1883 Mary's daughter Mary Elizabeth ("Mae") was born.
The following years were difficult, to say the least. In 1886, Herbert Edwin died, leaving Mary in severe financial trouble. She left Herbert W (just 7) with Barnardo's*, but kept Mae (3) with her. In 1890, Mary's father Richard died too.
In 1893, Mary remarried, to George Jenkins. Mary and George are in Camberwell in the 1901 census, with Mae. In the 1911 census, the three are in Lambeth, together with Mae's own daughter, my grandmother.
Ancestry's electoral registers have them in Deptford from 1922, through Mary's death in 1939 to George's death in 1956, in a house my mother remembers visiting. So Mary's location is fairly well mapped out, except during those dark years after 1886.
I can identify neither Mary nor Mae in the 1891 Census. George Jenkins was still living with his own parents in 1891, and Mary wasn't listed with him. Assuming she stayed as Mary E Richardson, I can't find a relevant-looking census entry, and I've looked through Mary's relatives, and Herbert E's family, and even George's family - she's not with any of them. I've checked the known addresses from 1881, 1886, 1893 and 1901, and she's not there. I've looked on Ancestry, FindMyPast and FamilySearch.
I have no reason to believe that Mary left London, although she could, for example, have gone to her Hill relatives in Gloucestershire. A country-wide search turns up nothing obvious, in any case. I am assuming that Mary kept Mae with her, although it is possible that she didn't, in which case identifying them may be even harder. There are numerous hits, even within Mary and Mae's age ranges of ~34 and ~8 in 1891, but none I've seen that look right.
So what new strategies should I be pursuing, or resources can I turn to?
*Herbert Walter ended up in Canada in 1893 under the Home Children programme. He stayed in touch with his family in the UK. One of his descendants has confirmed some of the above.
EDIT: An extra note that I should have included. "Mae" is is the name her family (her brother in particular) used. She is "Mary Elizabeth" on all records I've found so far - I used "Mary" and "Mae" here to distinguish mother and daughter. But it's possible that Mae/May is used in some records.
A summary of Mary's known timeline through the relevant period:
07 Apr 1861 Islington - Census - Mary, Richard, Annie, Richard D 02 Apr 1871 Hackney - Census - Mary, Richard, Annie. 12 Dec 1878 Hackney - Marriage - Mary and Herbert E Richardson 22 Mar 1879 Hackney - Birth - Son Herbert W 03 Apr 1881 Camberwell - Census - Mary, Herbert E, Herbert W 14 Jun 1883 Clapham - Birth - Daughter Mary E (Mae) 05 Sep 1886 Clapham - Death - Husband Herbert E 1886 - - Mary left Herbert W with Barnardo's 22 Aug 1890 - Death - Father Richard Hill 05 Apr 1891 NOT FOUND - Census - 21 Aug 1893 Southwark - Marriage - Mary and George Jenkins 31 Mar 1901 Camberwell - Census - Mary, George, Mae 31 Mar 1911 Lewisham - Census - Mary, George, Mae