Is there any chance that the father's name on your mother's birth certificate could have been Stanley Darnell rather than Darwell ?
Looking at BMD for births and marriages of a Stanley Darwell in England and Wales, the name is very rare. On the other hand, there are a few Stanley Darnells.
Then looking at the 1901 censuses for a Stanley Darnell in the right age group, there's only one showing up, and he just happens to be from a prosperous family ( which would fit with the "Gentleman of independent means")
1901 England, Surrey, Croydon, district 9, page 32
"Braemar", Campden Road
William Darnell head wid 63 corn merchant and wharfinger b Surrey, Bermondsey
Arthur R son unm 29
Catherine dau unm 29
Stanley son unm 27 corn merchant
all b Bermondsey
3 servants and a housekeeper
Food for thought, anyway.