The academic and 19th century politician George Pryme met Mr Pitt on several occasions when Pryme was attending Trinity College, Cambridge. In Pryme's memoirs, he describes presenting his prize-winning Greek Ode on the subject of Pompeii Columna to Mr Pitt at an 1802 Commencement ceremony at the Senate House in Cambridge. Pryme was then in his third year at Trinity, and Mr Pitt was the MP for Cambridge University. Pryme writes that Mr Pitt "received it [the printed Greek Ode] from me very courteously" (Pryme: 53).
He then proceeds to describe his recollections of Pitt:
"This was not the only occasion on which I saw Mr Pitt, for being Member for the University, he usually came there twice a year to visit his constituents. His stately form and cocked hat, then not quite obsolete, attracted the attention of every one. He is admirably represented by the statue in the Senate House, from the pedestal of which I can almost fancy him walking forth" (Pryme: 53).
Pryme himself later became a Member of Parliament for Cambridge.
Finally, at the bottom of pg. 53 of Pryme's posthumous memoirs which were edited by his daughter, there is an anecdote of Pitt which was supposedly derived from an extract in the Cambridge University Calendar for 1807. Here is the extract: "He [Pitt] had an almost military manner of walking as he put one foot before another" (Pryme, footnote on p. 53).
Having read the Cambridge University Calendar for 1807 and as well the years on either side of that date, I was unable to find the source for that enlightening little piece of information. That doesn't mean I don't believe it's true, though!
Pryme, G. (1870) Autobiographic Recollections of George Pryme, Esq. M.A. (edited by his daughter). Cambridge: Deighton, Bell & Co., p. 53.