Lucy Rose is all I have been listening to these few days.
If you are a fan of Bombay Bicycle Club, you would notice that her vocals are featured on their albums. (I bet she is dating Jack Steadman, the lead from Bombay Bicycle Club, who provides support vocals in this video)

I am such a sucker for female vocalists with distinctive voices who sweetly croon heartbreaking songs. Rachael Yamagata and Corinne Bailey Rae are perfect examples and my absolute favourites <3