Thames, Severn, Trent, Mersey, Tyne, Clyde, Shannon, Ouse, Avon, Wear. The Thames, Severn, and Tweed are the main rivers in the British Isles. Also, the Shannon River and the Wye River are well-known rivers in the British Isles.
The Tweed River forms the border between Queensland and New South Wales at its mouth. The majority of the Tweed is in New South Wales. Though irrelevant to the question, there is also a Tweed River in the UK, and one in New Zealand.