While there is not one singular “UK River Authority,” several organizations manage and monitor rivers in the United Kingdom.
For England: The Environment Agency website is the most comprehensive resource for river-related information in England: https://www.gov.uk/government/organisations/environment-agency
For Wales: Natural Resources Wales is the primary authority for rivers in Wales: https://naturalresources.wales/
For Scotland: The Scottish Environment Protection Agency (SEPA) is responsible for environmental protection, including rivers: https://www.sepa.org.uk/