Cleghorn was a popular player at Blackburn where his energetic performances at half-back were worth the admission price alone as described by a Blackburn historian: "A great little player who never knew when he was beaten. He worked like a demon, tackled effectively and headed the ball with wonderful skill. His value was enhanced by the judgement he displayed in feeding the forwards. On many occasions Cleghorn roused crowds to a frenzy of enthusiasm." Five ft. 5 in. (166 cm.) Cleghorn played 48 games for Rovers from 1894-1896 in the First Division.

Cleghorn made his debut for second division Liverpool on 21 March 1896 in a home fixture with Burton Swifts which Liverpool won 6-1. He played in the last six games of that successful season which saw Liverpool go up again. Cleghorn made a further 17 League appearances in 1896/97 before being one of the club's two 'ever-present' players, the other was 'keeper Harry Storer, in 1897/98. The next season was his final one at the club and he made six more League appearances to take his total up to 70. Cleghorn also played in ten FA Cup ties for Liverpool and his only senior goal for the club came in that competition, a 4-3 first round victory over Burton Swifts on 30 January 1897. After leaving Liverpool he won the Western and the Southern League with Portsmouth in 1901/02.