Slightly Sinful by Mary Balogh Book

Lord Alleyne Bedwyn is injured and suffers from amnesia after the Battle of Waterloo. He is found by Rachel York, a well-bred woman who is staying at a brothel after being swindled out of her inheritance. Alleyne and Rachel devise a scheme to help her regain her fortune, which involves them posing as a married couple, leading to humorous situations and a blossoming romance.