In this dystopian novel, humanity has become infertile, and the last child born in England, named "The Last Man" or "The One", was 21 years old when the book starts. The story follows a man named Theo Faron who is a former civil servant now living in a decaying society rife with violence and lawlessness.
While the book doesn't specifically mention a "two-child policy", there is a prevalent fear and paranoia about overpopulation and resource scarcity. In this context, families having more than two children would be highly frowned upon and likely considered illegal.
If you're interested in exploring further, you can also check out the film adaptation of "The Children of Men", directed by Alfonso Cuarón. While it takes some liberties with the plot, it stays true to the themes and atmosphere of the book.