Yep, done it a few times in a sportscruiser. As mentioned above, Oxford to St Kats in 2 days isn't possible, and you have to hit the St Kats lock in a 2 hour window.
A comfortable day on the upper Thames is 20 miles, a big day with 8-10 hours on the water is still only around 30 miles. Its around 90 miles from Oxford to Teddington alone and then you have the trip through London as well (another couple of hours).
If you have the time, its well worth doing it, but with those distances I would usually spend 10-14 days on that cruise. If you really want to go into London you can always get the train, we often cruise to Datchet Marina and then get the direct train (5 min walk to station and 50 min ride on train).
If you only have 2 days, set your sites a little lower. There is a great easy slip at Benson Waterfront near Shillingford, secure parking for car and trailer as well. You can then go up to Abingdon or Oxford and back in a weekend.
We love the Thames for a relaxed change, there is still something special about mooring a Riverside pub and not worrying about getting home.