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