Beardmore was born in Greenwich, London, in the family home. His father, also William Beardmore, was a mechanical engineer, working for the General Steam Navigation Company in Deptford. In 1861 his family moved to Glasgow, where his father bought the Parkhead Forge, a steel mill and supplier to the thriving shipbuilding and railway industries on the Clyde in the east end of the city.
Beardmore's origins are traced back to Greenwich, London, where he was born at his family home. His father, William Beardmore, worked as a mechanical engineer for the General Steam Navigation Company in Deptford before relocating the family to Glasgow. In Glasgow, his father acquired the Parkhead Forge, a steel mill that served the shipbuilding and railway industries on the Clyde.