The Leicester ring takes much more than a week to do, so if it will be a week it rules that out.
Loads of people do the Warwickshire ring in a 1 weeks hire, but you will need to put is a few decent days.
You will get tuition from them all (I hope), and depending on the company they will help you through your fist locks. It's not hard, so don't worry.
There are many hire companies on the ring, some suggestions to look at would be Kate Boats, Calcutt Boats, Napton Narrowboats, Black Prince (at Wigrams), Union Canal Carriers, Rose Narrowboats.