Arthur Willoughby Barton (14 September 1899 – 24 August 1976) was a headmaster, academic author and association football referee.

He was educated at Nottingham High School and then Trinity College, Cambridge, after military service with the Royal Engineers.

Barton was Chief Physics Master at Repton School from 1926 until 1939, when Geoffrey Fisher, later Archbishop of Canterbury, was headmaster.

While at Repton he was awarded a doctorate from the University of London for a thesis on radioactive decay (the measurement of the half-period of radium C).

[2] He refereed the semi-final between Austria and Poland in the 1936 Summer Olympic Games in Berlin, and was linesman in the 1936 FA Cup Final between Arsenal and Sheffield United.