The Wicked Rebel by Mary Lancaster

At eight-and-twenty, Lady Arabella Niven is gentle, sickly, and firmly on the shelf. Having disobliged her father by refusing her last chance of marriage, she has been sent in disgrace to Blackhaven with two domineering aunts. Her one wish is to be left alone in a quiet cottage to write books on history.
However, everything changes when she tries to rescue a naked man apparently drowning at sea. Thus begins an odd, fun friendship that quickly becomes passionate. For Captain Alban, the hero with a shady past, is rebellious and unconventional by nature.
Marriage between such a man and a duke’s daughter is inconceivable, and yet Alban’s feelings for her drive him to face his past in order to create a new future that would be unendurable without her.
Oppressive family, neglected children, fortune hunters, past loves, and old crimes all contrive to keep the pair apart. But when danger threatens Alban, it is the duke’s gentle daughter who rides to his rescue.