I think you may have the correct one, when I put in the information the same information came up but the name was Albert William Coote, not Coote Albert William, see below, hope this helps
Albert William Coote
Year of Registration: 1899
Quarter of Registration: Apr-May-Jun
District: Chelsea (1841-1981)
County: Greater London, London, Middlesex
Volume: 1a
Page: 422