Hm - actually, Baby May is recorded in censuses as Annie's niece.

(whoops, my carelessness -- that is what Doug's message said.)
In 1901, the two are in Islington, where Annie Parker is recorded as the married head of household, a swimming instructor, and May Waters as her niece.
In 1901, Frederick Waters appears to be a tram conductor boarding in Bromley and reporting himself (or perhaps the head of household assumed) as single. This is the only person who matches his description in 1901 (same age and place of birth as in 1891), and no one else in 1891 matches that description.
May Elizabeth Waters' birth was reg in Tunbridge reg dist in June quarter 1890. In 1891, she appears with parents Thomas, a cycle mechanic, and Kate in Tunbridge, Kent. Kate was born in Abingdon; she seems to have been Annie's sister then.
Thomas Truman Waters and Kate Elizabeth Luker married in Tunbridge in 1889.
Thomas Truman Waters died in 1898 in Tunbridge.
There is a Kate Waters marriage in Tunbridge in 1889.