Born in West Melton, West Riding of Yorkshire, Radford began his career in local league football with Wath Athletic, Wombwell and Darfield, before signing as a professional with Football League Third Division North side Nelson in December 1927.
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Radford scored all four goals in the 4–0 victory against Wrexham on 11 February, becoming only the second Nelson player, after Jimmy Hampson, to achieve the feat in a League match.
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