This book takes place in times where having the ability to swim is feared. Swimming is feared because there are monsters that live in the water that can disguise themselves as humans. The main character is a boy who is exiled from a city because he demonstrated the ability to swim after being pushed into the ocean. He finds work capturing monsters. In order to get to the monsters, he needs to climb down a long ladder. Eventually, he befriends a monster and he names it Digby. Near the end of the story, he becomes something like a knight and goes to war. The book ends when he fights in a battle and loses an important sword in the water.
The Well Between the Worlds by Sam Llewellyn.
The city of Lyonesse is sinking below the water. The water levels are to be controlled by wells. But the wells are inhabited by monsters. Idris Limpet, a peasant boy, is to be trained as a Monster Groom, a controller of the monsters. Law and order are administered by the Captains, who are both officious and somewhat unintelligent. Anyone of the human population who can swim is suspected of being a Cross, with monster blood.
Idris Limpet dives into the sea to rescue a boy, and therefore falls under suspicion. From this low point in his fortunes, aided by a girl called Morgan, he rises to become the King of Lyonesse. The name of Morgan is not the only link to Arthurian legend. The whole book may be seen as a retelling of the story of Pendragon. A light touch is added when Idris and Morgan befriend a small and not very menacing Monster named Digby.
I haven't actually read it, but the reviews talk about how human industry is based on exploitation of the monsters' ability to generate massive heat, and that the series (this is the first of the series) is essentially a retelling of the Arthur Pendragon story.