Hi Bob,
Welcome to the Forum.
Thanks for posting such a fascinating first post. I believe you have a pair of examples of the work of a noted English silversmith.......but, noted for all the wrong reasons.
Your castors purport to be the work of Thomas Parr II, an important silversmith of the 18th century and Warden of the Goldsmiths' Company. They bear the date mark, as you noted, of 1783, but this is where things start to go wrong. Thomas Parr II, was probably dead, or at least retired by this date, also the cartouche that surrounds the date letter is usually only to be found on small articles.
The actual maker of your castors could well be Charles Twinam, who was known to use the 'TP' mark on some of his output, if so, they probably date to around c.1890.
Of course, this is just my opinion and it would be good to hear the thoughts of others.
In the meantime, below are the links to a couple of articles that explain more about Charles Twinam and the reasons for his initial success:
http://www.925-1000.com/a_Spurious1899.htmlhttp://www.925-1000.com/a_OB_Twinam1899.htmlTrev.