The Department of Health and Social Services may order and direct that the owner of any property on which there is a cesspool or privy well and all other drainage already in use in any incorporated town or within 1 mile from the water supply of the town shall so change and construct the same out of brick and cement or concrete in such manner as to prevent the contents thereof from oozing through or passing into the soil around the cesspool or privy well or from overflowing over the top thereof.