Bramwell is not exactly a common surname in Scotland, there are only 119 Bramwell births on ScotlandsPeople for the entire period of statutory registration of births from 1855 onward. No sign of a Joan Bramwell, but there is a Raymond Bramwell born in 1933, who's birth was registered in the Ardrossan Old registration district, which is certainly in Ayrshire and not too far from Largs. Looking for other Bramwell births in the Ardrossan Old registration district then produces a Helen Joan Bramwell born the following year in 1934.
Because both births fall within the 100-year limitation on viewing birth registrations online on ScotlandsPeople you'd have to order copies of one or both birth registrations, but this would give you both their parents' names and when and where they married.
Edited to add that there is no obvious Bramwell marriage on ScotlandsPeople that would fit with these births, either location- or date-wise.