The Pearl of Gladstone by Barbara Russell

London, 1884:

Accused of being involved in her father’s bankruptcy and wanted by the police, Pearl finds herself penniless and jobless. Her father disappeared, leaving her alone to sort out a financial mess she doesn’t know anything about. Heck, she doesn’t even understand what her charges are.
Desperate, she asks for a job to Miss Cherrywood, the head of a secret society—The Wayward Ladies—dedicated to aid women in need.
The job Miss Cherrywood offers is simple, but borders to felony. Pearl is supposed to impersonate Miss Amelia whose parents wish her to meet brooding and short-tempered Lord Christopher Lyon, Earl of Gladstone. Lacking the courage to disobey her parents and to reject Christopher, Amelia begs Pearl to help her. Pearl isn’t exactly eager to add more crimes to her already growing list. But Christopher—whose best friend is a former business partner of her father—might be her only chance to learn in what trouble her father is and to find him.

Lord Christopher Lyon doesn’t want to meet any woman, especially this Miss Amelia whose mother keeps writing letters to him, guaranteeing that he and her precious daughter are a perfect match. Not likely. Which woman would find a temperamental, disfigured soldier, just returned from war, interesting? On top of that, he’s investigating a financial fraud that has destroyed his friend’s finances. He doesn’t have time for meeting ladies.
Determined to find her father and clear her name, Pearl accepts to play the part of Miss Amelia and beard the Lyon in his den.