Bradford was born at Carwood House, Witton Park, Bishop Auckland, the son of a colliery manager. The 1914-18 war gave Bradford a chance to realise his military ambitions. He showed remarkable ability and won the MC in 1915. By 1916 he was a lieutenant-colonel and won the Victoria Cross. In 1917 he was promoted brigadier-general. and became the youngest general in the British army. He was killed in action in November 1917. There are memorials to Bradford in several places in Darlington.

Two of Bradford's brothers were killed in the war. His brother James won the MC while George, a lieutenant-commander in the Royal Navy was killed in the Zeebrugge raid in 1918. He was awarded a posthumous VC. The General Bradford Memorial Fund was opened to honour the three brothers and the contributions used to build the Bradford entrance at Darlington Memorial Hospital.