Greenhalgh was born in Mansfield and played for Notts County, before the foundation of The Football League, from 1869 to 1883 making over 147 appearances as a defender and was made Captain in 1872. His arrival at Notts County in 1869 helped to "greatly improve (their) results, due mainly to his great influence and leadership".
He was one of only two players not from a London-based or university team to be chosen by the England selectors for the match against Scotland on 30 November 1872. In this match he played as the only full back in a 1-1-8 or 1-2-7 formation and was Notts County's first international representative. From the eleven who played in the first international, the England selectors only recalled Greenhalgh and Charles Chenery for the return match on 8 March 1873, which resulted in a 4-2 victory for England.
After retiring from playing in 1883, Greenhalgh continued to play an important part in the development of football, helping to found Greenhalgh's F.C. in Mansfield. He was also the owner of Field Mill in Mansfield which was the home of Mansfield Mechanics F.C., until becoming the home of Mansfield Town in 1916.
- "England National Football Team Match No. 1". England Football Online. Retrieved 20 January 2008.
- Notts County a Pictorial History page 8 ISBN 0-9547830-3-4
- Gibbons, Philip (2001). Association Football in Victorian England - A History of the Game from 1863 to 1900. Upfront Publishing. p. 20. ISBN 1-84426-035-6.
- "Club Affiliations - Notts County". England Football Online. Retrieved 20 January 2008.
- Graham Betts (2006). England: Player by player. Green Umbrella Publishing. p. 114. ISBN 1-905009-63-1.
- 1901 Census
- 1881, 1891 & 1901Census
- 1911 Census