Mike beat me to it. Unless you are experienced - several trips - with running a narrowboat it is not recommended by most hire companies or publishers, or experienced narrowboaters (I've taken several over the years and I don't think I'm sufficiently qualified) to take a boat on a tidal river like the Thames. Even that far upstream. The river behaves completely differently than a canal after a rain, during a dry spell, and during tide movements. The banks are very different, and there are invisible currents due to the everchanging bottom. Canals are much more predictable and can be operated by most people with a modicum of instruction and attention.
I've never worked boats on the Oxford Canal or the River Cherwell but I'd love to one day. I can recommend wholeheartedly the Stratford Canal (Stratford-upon-Avon to Braunston) but be careful if somebody wants to sit up top - those bridges are LOW..
Black Prince is well respected, as are several others including Alvechurch. Sometimes a small operation with only a few boats can do a good job. Look at their webpages and look carefully at the fitout of the boats.
Hard work, narrowboating, but ever so relaxing and pleasant. (gets a bit wet from time to time, most marinas include waterproofs but probably best to bring your own if you aren't one-size-fits-all).