Does anybody know the name of Mr. Whitworth?
Whitworth, as in Rudge Whitworth, derives from the Birmingham "Whitworth Cycle Company" the origins of which were with Charles H Pugh Ltd of the Whitworth Works in Birmingham. They were manufacturers of screws and such-like, so I'd guess that the works was named Whitworth after (Sir) Joseph Whitworth, best known in connection with his development of a rationalised system of screw threads and for the screw threads that bear his name.
That is to say, I'm pretty sure there was no Mr Whitworth in the foundation of the Whitworth Cycle Co, but there was a Daniel Rudge (1841-1880), whose company Rudge Cycles was amalgamated with Whitworth.