Can anyone name this book?

I'm sorry this is vague but I heard about this book awhile ago and forgot the title can anyone help me out? Its about a young afro caribbean woman who emigrates by boat to london and becomes a mistress to rich men which she lives a good life from - it is a fiction book not a biography (I think). It is possibly set in pre - WW 2 but im not sure of the exact time frame.It was also reviewed on BBC radio 4 a few months back. Sorry its very vague but any help is appreciated!!