After being rejected by Barnsley, he joined Leeds United in 1929. He soon became a regular in the Leeds back line, and made his debut for England, against Italy on 13 May 1933.
He played over 160 League games for Leeds in five seasons. Copping joined Arsenal in the summer of 1934, and immediately took a first-team place at left half; he was an ever-present in his first season for the club, until suffering a serious injury in the third-last match of the season against Everton; Copping soldiered on to ensure Arsenal would win, which they did 2-0; this greatly helped the club to the 1934-35 First Division title.
He was also one of seven Arsenal players to start England's match against Italy in November 1934 (the "Battle of Highbury"). Copping went on to win the FA Cup in 1936 and another League title in 1938. Copping remained a near-ever present for Arsenal up until the spring of 1939.
With World War Two looming, Copping put in a transfer request so that he could return to the North with his family. Arsenal duly complied, and Copping re-signed for Leeds United, playing out the rest of the 1938-39 season.
Copping joined the Army at the start of the war, and served in North Africa, eventually becoming a Sergeant Major. He played the odd wartime game for Leeds, but retired from playing football in 1942.
Despite his nickname, the "Iron Man", and his hardman image (he took to the field unshaven, a remarkably unusual practice at the time), Copping was never booked or sent off in his career.
In all he played 189 matches for Arsenal, and 20 times for England. After the war ended, Copping became a trainer and coach at various clubs, including Beerschot in Belgium, Southend United, Bristol City and Coventry City.
He retired to live in Southend-on-Sea. He died in 1980, aged 70. In 1998, the Football League, as part of its centenary season celebrations, included Copping on its list of "100 League Legends".