The Devil May Care by Emma V. Leech

Dishonoured and ashamed, the ton’s scandalous darling, ‘Beau’ the Marquis of Beaumont, is forced to flee England to escape debtor’s prison.
After a chance encounter, it appears Miss Millicent Sparrow is his only remaining friend, however unlikely.
Miss Sparrow lives up to her name. Damaged and terrified by her cousin’s violent abuse, Milly is used to being overlooked and prefers it that way, until the desperation of her bleak world is gilded by rakishly handsome Beau’s extraordinary friendship.
Miss Sparrow’s lively letters help Beau through his banishment and when his father dies suddenly and Beau inherits the Dukedom, he seeks out his little bird. To his shock he finds a woman in despair and, moved by pity, he offers her the protection of his name by marriage.
But Milly becomes impossible to overlook, and the more Beau needs his wife, the less interested she seems in her gorgeous husband.
For this rake, getting a woman’s attention has never been so complicated.