Arthur James Cook (1883 - 1931), known as A. J. Cook, was a British coal miner and trade union leader. Born in Somerset in England, he moved to Rhondda in South Wales to work in the mines at the age of sixteen. He was General Secretary of the Miners’ Federation of Great Britain from 1924 until 1931, a period that included the 1926 General Strike.

He famously set out the miners' demands as "not a penny off the pay, not a second [often quoted as "minute"] on the day".