She was reputedly the illegitimate daughter of Prince Adolphus, 2nd Duke of Teck and 1st Marquess of Cambridge, by Rosa Baring. I have managed to work out how these two probably knew each other and why they might have met at the time around Vera's conception. I have amended her Wikipedia article accordingly. See:
I have also realized that Vera might have acted as a go-between between Churchill and Mussolini during WW2. I have also added this to the article.
I would welcome people's views on these matters.
PS I have also found that Vera was described as 'adopted' in the 1891 census. This is the first official indication that she was not the legitimate issue of her legal parents.