The River Cherwell is the River in Oxford where Lyra frequently swam with Roger.
The River Isis is a river in Lyra's Oxford used for transporting goods and merchandise. It is equivalent to the River Thames in our world. The Thames has traditionally been called the Isis where it passes through Oxford. Philip Pullman has extended the name to cover the whole Thames right down to London. In describing its course in The Golden Compass he mentions the Thames-side towns of Henley, Maidenhead and Teddington, but not the much larger and rather less fragranted towns of Reading and Slough.