Florence Washburn is engaged to Kit Swinton. Kit is the younger son of an earl and a rising star in diplomacy. He will be perfect for Florence, since she is intelligent and keenly interested in politics - so what if she does not love him - at least they suit. Since Kit is overseas, the wedding will have to be a proxy one with Kit's older brother Thomas, Viscount Alford as the stand-in groom.
Alford is a rake and a rogue who spends his time drinking, gambling and carousing with dancers. Florence despises him and he only remembers her as the annoying little girl who used to follow him and Kit around. When the wedding papers come to Alford to sign, he is too vain to wear his glasses in front of his friends and signs on the wrong line - not the proxy, but the groom. Since the wedding ceremony has been performed, he and Florence are married.
Alford and Florence are horrified - they hate each other! So their families send them off to the country while they arrange a quiet annulment, but Alford and Florence end up at the same estate (seems their families know them better than they know themselves).
Most of the rest of Married By Mistake shows how Florence and Alford discover the truth about each other's characters and how very well suited they are for each other. There is a bit of farce about how the estate is haunted and an episode that involves the locals who make a living smuggling French brandy to England. Both of these plot threads serve to shed light on Florence and Alford and add much to the story. It all ends up as a total delight.