Son of a forge labourer, Eli joined the army at sixteen in 1912 and served through the Great War with the 2nd Battalion, East Yorkshire Regiment in France, the Balkans and the Middle East. Signing for Crewe Alexandra on the resumption of football he switched to Macclesfield Town in November 1920 before joining Exeter City ahead of the club’s second season in the Football League. 

Making his City debut in the opening day defeat at Charlton Athletic on 27 August 1921, Eli scored his first goal against Newport County on the final day of the year. Released at the end of the season after making 27 league appearances, he returned to Cheshire to play for Macclesfield Town ahead of finishing his career with Runcorn.

Eli received an army pension for deafness, an hereditary condition (otitis media) which may have been exacerbated by the war.

Eli Bullock died in Staffordshire in 1984.