The novel has a complex plot, common in Collins’ work. In a Prologue, a selfish and ambitious man casts off his wife in order to marry a wealthier and better-connected woman, by taking advantage of a loophole in the marriage laws of Ireland.
The initial action takes place in the widowed Lady Lundie's house in Scotland. Geoffrey Delamayn has promised marriage to his lover Anne Silvester (governess to Lady Lundie's stepdaughter Blanche), who has incurred the enmity of her employer. The spendthrift Geoffrey is about to be disinherited, and wishes to escape from his promise and marry a wealthy wife. Nevertheless he is obliged to arrange a rendezvous with Anne, in the character of his wife, at an inn, and documents this in an exchange of notes with her. Subsequently, urgent matters force him to send his friend Arnold Brinkworth, Blanche's fiancé, to Anne in his place. To gain access to her, Arnold must ask for "his wife". Although nothing improper passes between them, they appear to the landlady and to Bishopriggs, a waiter, to be man and wife.
Thus both Geoffrey and Arnold might be deemed to be married to Anne, depending on the weight put on the spoken and written evidence. Most of the novel concerns Anne's, Geoffrey's and Arnold's attempts to clarify their marital status:
Anne needs to be married to save her reputation
Geoffrey wishes to cast off Anne by asserting that she is married to Arnold
Arnold wishes to marry Blanche, but fears he has accidentally already married Anne under Scots law.
In subsequent chapters Geoffrey, a keen athlete, courts Mrs Glenarm, a wealthy young widow, while Anne consults lawyers who give her conflicting advice about her position, and later tries to explain the situation to Mrs Glenarm, who rebuffs her. Arnold seeks the advice of Lady Lundie’s brother-in-law Sir Patrick Lundie, a retired lawyer. Sir Patrick approaches the problem with energy, but owing to various mishaps, Geoffrey’s determination that his scheme shall succeed, and the unsatisfactory state of the law, is not immediately successful. However he ascertains that the correspondence linking Geoffrey and Anne exists and was stolen at the inn by Bishopriggs, who tries to extort money for it. Anne, who strongly wishes to remove any impediment to Blanche and Arnold’s marriage, comes to the same conclusion and forces Bishopriggs to give her the letter by threatening to reveal its contents, which would make it worthless for blackmail. Eventually Anne offers to reveal her relations with Geoffrey, even at the cost of her reputation – impressing Sir Patrick with her courageous and honourable behaviour. At a meeting of all the parties and their lawyers, she makes her revelations. Geoffrey can no longer avoid honouring his promise to her and acknowledges her as his wife.
A sub-plot concerns Geoffrey’s athleticism. While training for an important race, Geoffrey is discovered to have a serious physical ailment rendering him liable to a paralytic stroke. In the race itself, in which Geoffrey represents the South of England against the North, he collapses near the end, leaving his opponent the victor. His “friends” desert him, having lost their bets placed on him.
The novel finally becomes a thriller. Geoffrey takes Anne to a secluded cottage in which the cook-housekeeper Hester Dethridge (who also features in the earliest scenes) is mute. Hester inadvertently reveals to Geoffrey that she murdered her brutal and rapacious husband by dismantling part of the wall of his (locked) bedroom in an almost-invisible way, leaning through and smothering him. Geoffrey forces Hester to show him how to do the same to Anne. By various stratagems he gets Anne to sleep in a suitably-placed bed. However he suffers a stroke when about to smother her, and while unconscious is throttled by Hester, who belatedly recognises the enormity of what she has been abetting. Sir Patrick, knowing the danger in which Anne is placed, has kept watch outside the house and, when Anne gives the alarm, duly rescues her.
In the final scene, Lady Lundie awaits a visit from Sir Patrick and his new bride. She is chagrined to discover that the lady in question, who takes precedence over her in the family, is her enemy Anne.

Question: Why couldn't Arnold marry Blanche right away?
Answer: He was afraid that he accidentally married Anne under Scots law.
Alternative answer: He was afraid he married Ann under Scot's law.