I have read that the reason is that British river names are some of the oldest names still in use today. Because it was customary for the Romans to assign local names, usually the names of rivers, to their forts we know what the names of those rivers must have been before they arrived. It seems that the British adopted the Roman way of naming their rivers as in Latin the word "river"comes first, then its name follows. The Americans and Australians use the names of their rivers as adjectives to describe their rivers. Perhaps someone else has got another explanation?

Good observation! I think it is for linguistic reasons,it is a typical British way to put it (River first). If you checked Canadian Rivers ( Back River) or Australian ones ( Barcoo River) you will find the word 'river' also coming after.

Good question. I have absolutely no idea.