Only You by Elizabeth St. Michel

Nicholas, heir to the Duke of Rutland, has been kidnapped. Imprisoned aboard a Portuguese slaver, Nicholas learns that his family members have been either captured or slain—but a mysterious woman allays his despair.
Fellow prisoner Alexandra has overheard that his family is safe. But can he believe her? She claims to be a woman of status, but as she cannot prove her story, Nicholas assumes she is a thief. They are in the same predicament, however, and he and Alexandra form a friendship.

When a hurricane destroys the ship and Alexandra rescues Nicholas from certain death, he must discover the truth about her. They wash up on a deserted island, where her survival skills come to the fore. As an aristocrat, Nicholas feels unequipped to handle the situation, but he watches Alexandra with growing admiration—and hears her account of how she, the daughter of a baron, came to be so resourceful.
Nicholas yearns to leave the island and seek revenge on his captors, yet he can no longer deny his growing passion for Alexandra. Of noble birth herself, she is an appropriate match for Nicholas. Yet Alexandra has more secrets—and one of them could doom their love.