I think there's something in these records to consider.
1901, Eastbourne. RG13; Piece: 883; Folio: 46; Page: 31
James Watson 73, Westham, Sussex
Edith Searle 35, dau, Westham
Ernest Watson 18, son, Westham
Bertram Searle 6, grandson, Eastbourne
Sidney Searle 5, grandson, Eastbourne
May (or Mary) Searle 3, granddaughter, Eastbourne
1891, Eastbourne, RG12; Piece: 774; Folio: 106; Page: 32
James Watson 63
Edith Watson 25
George Watson 24
Frederick Watson 18
Ernest F Watson 8
Marriages Dec 1895
Edith Watson, also listed Sydney John Searle.
My opinion is that as Bertram was born (1894) before Edith and Sydney married, he was registered Watson, Sydney Searle may not be his biological father.
SEARLE, SIDNEY ALBERT, MMN WATSON
GRO Reference: 1896 J Quarter in EASTBOURNE Volume 02B Page 74