When Dodgin Sr. moved to Fulham in 1949, his son followed him there, although he still had to wait two years before making his debut in December 1951, against Preston North End at left back.
Feeling the pressure from the fans (who questioned whether he would have been picked, were his father not manager), Dodgin transferred to Arsenal for a fee of £4,000 in December 1952,[2] having played 35 League matches for the Cottagers.
[3] After the departure of regular centre half Ray Daniel to Sunderland that summer, Dodgin became first choice at the back for Arsenal, missing only three matches that season.
After retiring from the game, Dodgin became a coach, first at Millwall, then at Queens Park Rangers, where the club had its 1967 League Cup win.
During his tenure at Loftus Road, he presided over the club's worst start in its history, a run of 12 games without a win.