Depends on where the river is and exactly what you mean by dirty. If you are talking about pollution, who you report it to will depend on where in the UK you are. Here is some info..
If you mean litter - in the river or on the bank - then that may well be the responsibility of the landowner. More info here..
Whether anyone has a responsibility to clear it up will depend on what it is, where it is and how much of an issue it it causing.