To summarise the family (previous thread link posted by carol8353) and add detail:
Harry G W VERNON born Mar qtr 1907 Islington vol 1b p189 (11 Feb). Parents Harry James VERNON and Sarah Amy VERNON (formerly COOK)
Sarah Amy COOK married George Edwin BOLTON Dec qtr 1887 Islington vol 1b p461
BOLTON/COOK children (as per GRO index):
Amy Elizabeth Mar qtr 1888 Holborn vol 1b p802 (bapt 1893)
Maud Alice Dec qtr 1889 Holborn vol 1b p760 d Jun qtr 1890 Holborn age 0
Mary Emma Sep qtr 1891 Shoreditch vol 1c p87 (bapt 1892 d Mar qtr 1892 Holborn age 0
Emma Ethel Sep qtr 1893 Holborn vol 1b p675 (bapt 1893)
Edwin William Dec qtr 1894 Holborn vol 1b p723 d Mar qtr 1895 age 0
Jennie Alice Jun qtr 1896 Holborn vol 1b p736 d Sep qtr 1896 Holborn age 0
Nellie Maud Mar qtr 1898 Holborn vol 1b p746
Henry James Jun qtr 1899 Holborn vol 1b p768 ?d Sep qtr 1899 Pancras age 0
(NOTE: the entries in italics are confirmed by baptism records or censuses, the others are "probables" as the parents' first names are not known)
Two children appear on censuses with grandparents William & Elizabeth COOK - 1891: Amy (3), 1901: Amy (13) and Nellie (3)
The 1911 census shows Amy VERNON (presumably Sarah Amy) age 43 born Birmingham together with Emma age 18, Nellie age 13, and Harry age 5. They are in the household of Alfred GROSCH, 49, head, housepainter, born Barnesbury.
This gives a probable birth for Sarah Amy COOK, Mar qtr 1888 Aston vol 6d p620 mmn NEWBOULD
Harry James VERNON was described on son Harry's birth certificate as a "pianoforte fitter-up" but has not yet been found on censuses.
The main unanswered questions seem to be:
Did Sarah Amy COOK/VERNON marry Harry James VERNON?
Can Sarah Amy and a spouse be found on the 1891 and 1901 censuses?
Can Harry James VERNON be found on any census? An age and birthplace are essential to trace his parentage.