The law was even stricter than “no divorce.” A marriage proposal was considered a binding contract on the man (who did the asking; women never did). If a man asked a woman to marry her, and then denied doing so, or did something like proposing to someone else, the woman could sue him for breach of contract. He could settle by marrying her, or he could take his chances in court. If he lost, he’d probably end up paying her a lot of money. It might even be a stipend that was a lot like alimony, and continued until she married someone else.
A woman could always choose to release a man from his promise, however. If you have read PG Wodehouse, and wondered about all the backstage machinations Bertie Wooster went through trying to get a woman to break of an engagement he’d gotten into accidentally, instead of just telling her “Sorry, mistake,” it was because he didn’t want to be sued for breach of contract.