Born in Bradford to Irish parents, O'Callaghan was spotted by Doncaster Rovers playing for Bradford Boys and Yorkshire schools. But the offer to become a professional footballer was a tough decision to make for O'Callaghan as he had been accepted into Loughborough College to undertake a physical education teaching diploma. He signed the contract, deferring college for a year in case the football did not work out. After six months in Donny's reserves he was promoted to the first team and he developed a fine partnership with Peter Kitchen and he top scored in 1975–76 with 28 goals. By the time his goal tally had reached 77 for Doncaster he had attracted the attentions of bigger clubs and on 1 March 1978 Stoke City managerAlan Durban signed him for £40,000. The following Wednesday O'Callaghan was on the bench as Stoke struggled to break down a resolute Hull City and with time running out and Stoke winning a corner Durban decided to bring O'Callaghan on for his début. From the resulting corner he headed past Eddie Blackburn to make him an instant hero. He ended the 1977–78 season with six goals and was top-scorer in 1978–79 with 16 as Stoke won promotion to the First Division. With Stoke making a slow start in 1980–81 Durban moved O'Callaghan, who had lost his place to the younger Lee Chapman, to centre back filling in for the injured Denis Smith. He adapted well and his partnership with Mike Doyle saw Stoke in to a final mid-table position of 11th. He began the 1981–82 season in defence before reverting to forward in January 1982 where he scored five goals and he again scored five in 1982–83. He struggled under Richie Barker's long balltactics in 1983–84 and he handed in a transfer request but Barker was sacked and replaced by Bill Asprey and so O'Callaghan stayed at Stoke. Under Asprey Stoke staged a relegation survival but in 1984–85 Stoke were awful and well on their way to an embarrassing relegation so O'Callaghan moved on to Oldham Athletic for £30,000 after making 294 appearances for Stoke scoring 47 goals. In the first match of the 1985–86 he suffered an adductor muscle strain which caused him to retire on the advice of doctors.
Tall at and weighing over, 'Big Bren', as he was known, worked well as a willing target man, shielding the ball and acting as a link between midfield and a pacey striker.
