In 1911 living in Fulham were
John Collins 48 b Peckham
Elizabeth Collins 50 married 23 yrs, 5 children 4 living, b Shepreth
John Collins son single 26 b Sydenham
Mary Collins dau 6 b Fulham
Margaret Adams visitor 38 marr 11 yrs 2 children both living b Shepreth
Smith Adams visitor 10 b Fowlmere
Cecil Adams visitor 3 b Shepreth
John Collins appears to have married Elizabeth Collins in St Saviour in March 1888
All of which seems to firmly link Margeret and Smith to the Collins family. But I would be patient and wait for the birth cert.
I am told by Smiths Grandson that his grandmothers maiden name was Flack. However I cannot find any records of a Margaret R Flack. Is anyone able to shed any light on this while I am waiting for the certificate to arrive?
My reading of what you've written is that Smith Adams married a Flack (although I can't find such a marriage), not that Smith's mother was a Flack.