Higham made his League debut at the age of 20, making 2 appearances for The Saddlers before signing for Wolves. He made 38 appearances at Molineux, primarily as cover, before being bought by City. He was an impressive right half in his first season, establishing a half back partnership with Norman Dinsdale and Billy Bell, in City's best season since joining the League.

The arrival of Jimmy Baker from Wolves, pushed Higham into the reserves. Consequently, his appearances in his second season came only as a replacement for the injured Dinsdale. Higham was able to fit into the centre half position as he stood 6ft linch tall and weighed 12½ stone. He made no first team appearances at Lincoln.