The Undesirable Duke by Rose Pearson

A Duke disgraced by whispers. A Lady drawn to his side. Can they silence the rumors and find love at last?
Samuel, the Duke of Yarmouth, is stunned to learn that rumors about his supposed gambling, financial ruin and visiting undesirable haunts have been swirling through London. Unaware of where they have come from, he determines to go there for Christmas so he might not only unmask the culprit but bring about a return to his otherwise shining reputation.

Lillian knows she ought not to go near the Duke of Yarmouth given that she is meant to be seeking an excellent match, but something about him calls to her. While everyone else in society shuns him, she begins to offer him a little of her attentions whenever she can. Determining to help him, Lillian must battle the wrath of her overbearing mother as well as the desire within her own heart!