James Patrick Stephen Branagan was born in Urmston on 3 July 1955. His father Ken was also a full-back and played for Manchester City and Oldham. Branagan came through the juniors at Oldham and signed professionally in June 1973. He captained the reserve side but had limited opportunities in the first team.
After 27 appearances he moved to South Africa with Cape Town City. In November 1977 Branagan joined Huddersfield and made 38 appearances in two years as the club finished mid table in Division Four.
In October 1979 Branagan joined Blackburn for a fee of £20,000 and played in defence and midfield. He helped Blackburn win promotion to Division Two in 1979/80 when they finished runners-up to Grimsby. Rovers just missed promotion to Division One the following season when they finised fourth. On occasions Branagan captained Blackburn and stayed for seven and a half years making 294 league appearances and netted 5 goals.
In May 1987 Branagan joined Preston and made his debut on the opening day of the 1987/88 season in a 1-0 defeat at home to Chesterfield on 15 August. He was replaced on his second appearance a week later in a 3-1 defeat at Bristol City. His last appearance was a 1-1 draw at York on 12 September.
It was York who Branagan joined in October 1987 and in two seasons he scored once in 42 appearances. His first season he could help York avoid relegation to Division Four. Branagan then moved into non league with Chorley.