There is a possible death Dec 1/4 1887 of John Adams aged 51 in Pancras district.
There's a corresponding 'parish' burial 11th October at St Pancras Cemetery of John Adams, aged 51, who died at Highgate Infirmary, Pancras.
Ties up with the family having little or no money but no occupation is shown.
However, according to the Pancras Board of Guardians children at Leavesden records 2 supposed sons, Thomas & Alfred Adams or Simmonds, mother Emma so you may be able to rule that death out.
Moving on to Sarah and Jane though, they are on the same register. It isn't transcribed so a case of scrolling through on Ancestry
London, England, Poor Law and Board of Guardian Records, 1430-1930
select Camden
select St Pancras
select Register of Children
Leavesden School: register of children received from the Guardianīs office, 1880-1894
page 9 of 325
Sarah born 1880 was admitthed 4 April 1889, having been sent to Rottingdean Workhouse 6 Apr 1888, discharged 26 Aug 1892 back to her mother, Sarah Adams a widow.
Jane born 1879 was admitted 14 Jan 1892 from Rottingdean. She was also discarged to her mother 26 Aug 1892.
Several crossed out addresses leaving 33 Drummond ?
The Boards of Guardians were very good at charging other Boards for people that weren't of their parish so I wonder how Rottingdean fits in? Whether the mother was from there or did the Board of Guardians have an understanding for the children to be sent there?