Spradbery was born in East Dulwich and moved to Walthamstow as a child. We studied at Walthamstow School of Art where he later taught. He was a committed pacifist, serving with the Royal Army Medical Corps during the First Wold War and was awarded the Distinguished Conduct Medal for leading a stretcher party under fire. He later became a supporter of the Campaign for Nuclear Disarmament.
Spradbery specialised in landscape painting, in particular the countryside around Epping Forest close to his home in Buckhurst Hill. In addition to his design for London Transport, he received commissions from LNER and Southern Railway. In 1970 a memorial exhibition was held at the William Morris Gallery in Walthamstow; Spradbery had campaigned for the establishment of the Gallery to honour the designer, writer and socialist William Morris.