Angus was born in Amble, Northumberland and played for the local boys' club before being signed by Burnley as an amateur at the age of 16[3] in 1954.

A week after that debut, however, he was called into the first team after the club were hit with a number of injuries and he performed well in a 2–1 victory against Everton on 3 September 1956 giving international winger Tommy Eglington a difficult time.

His full cap came on 27 May 1961, when he and Burnley teammate Brian Miller made their England debuts in the same game against Austria in Vienna.

Angus continued his good form for Burnley as the title winning team was dismantled, and he had almost reached the age of 30 before his place was under threat.

He had played in a total of 439 league games for Burnley and, with cup games, totalled 521 appearances, which placed him as the outfield player with most appearances for the club at the time, behind only goalkeeper Jerry Dawson.