The navigational authority for this waterway is Environment Agency
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Wikipedia has a page about River Medway
The River Medway is a river in South East England. It rises in the High Weald, Sussex, and flows through Tonbridge, Maidstone and the Medway conurbation in Kent before emptying into the Thames Estuary near Sheerness, a total distance of 70 miles (113 km). About 13 miles (21 km) of the river lies in Sussex, with the remainder being in Kent.
It has a catchment area of 930 square miles (2,409 km2), the largest in southern England after the Thames. The map opposite shows only the major tributaries: a more detailed map shows the extensive network of smaller streams feeding into the main river. Those tributaries rise from points along the North Downs, the Weald and Ashdown Forest.