He made his League debut in the 0–1 defeat to Doncaster Rovers on 17 December, and scored his first three goals for Nelson on 7 January 1928 as the side beat Rochdale 6–3.
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.
He was signed by Football League First Division club Sheffield United in the summer of 1929, but found first-team opportunities limited there and only played 20 matches in two seasons, although he did score 7 goals for the side.
Radford subsequently spent a season with Northampton Town, but played in the reserves for most of the campaign, making just eight league appearances.
He was released in the summer of 1932 and later moved into amateur football, initially with the Royal Navy Depot in Chatham, Kent.