Kilbirnie, Ayrshire born wing half Harry Brandon joined St Mirren in 1888 from Heywood Wanderers moving to Clyde in 1889, before moving South to join First Division Sheffield Wednesday in the 1892 close season, and he made his Football League debut at Notts County in September 1892. He played six seasons at The Wednesday, playing with his brother Tom during the 1892-93 campaign, and was part of their FA Cup winning team of 1896 when they beat Wolverhampton Wanderers 2-1 in the Final at Crystal Palace. He was also twice a losing semi finalist with Wednesday in 1894 and 1895, when they lost respectively to Bolton Wanderers and West Bromwich Albion. He scored 15 goals in 166 games for The Owls before joining Chesterfield Town in 1898.
He was the younger brother of Tom Brandon of St Mirren, Blackburn Rovers, The Wednesday and Scotland, and the uncle of Tom Brandon Jr.