I suggested that you join the facebook page for the Association of Model Barge Owners, I do not know of one for Thames River barges.
A Thames barge in it's simplest form has a foresail, a mainsail, a topsail and a tiny mizzen. The foresail looks after itself, the topsail is controlled in conjunction with the mainsail by using two lines joined together and the mizzen is ignored. The mast is in two more or less equal parts, mainmast and the topmast, which can be raised or lowered. If you are building a simple representation, then the number of blocks etc required is nowhere near what it looks. As I've suggested before, look at lots of pictures of sailing barges. They are not difficult to build or rig and normally sail well. Unless you are looking for perfection, there is no need to build right down to the most minute detail, they will sail just as well.