Troedyrhiw, Merthyr Tydfil, Glamorgan born inside forward Viv Woodward represented Wales at schoolboy level and began his football career with Troedyrhiw in 1932 and joined Folkestone in 1933, where his senior football debut came in a First Round proper FA Cup tie at Brighton & Hove Albion in November 1934. Woodard was signed by Second Division Fulham in January 1936 season in a £300 deal, making his Football League debut at Leicester City the same March. It wasn’t until March 1937 that he established himself in the team, and in 1937-38 he scored 15 goals for the club in 33 League appearances finishing second top of The Cottagers’ goalscoring charts to Ronnie Rooke. By the time competitive football was suspended due to the outbreak of the Second World War in September 1939, Woodward had made 86 appearances and scored 26 goals for Fulham, and during the War he represented Wales in a wartime international on 7th June 1941, scoring in a 3-2 defeat to England at Ninian Park.
He resumed his professional career with Fulham after the War, playing twice in the 1946 FA Cup, but managed just 10 League appearances during the 1946-47 season before departing the club for Second Division Millwall in February 1947 after 11 years at the club. He scored seven goals in 15 League games to help The Lions stave off relegation in the run in to the season’s end, but he was in and out of the team during the 1947-48 campaign, scoring six goals in 27 appearances and when Millwall were relegated at the end of the season he departed the club to join Brentford in July 1948.
He found opportunities limited at Griffin Park, making just 10 appearances per season in each of his two seasons there, scoring 4 goals, before joining Aldershot in February 1950. He had a season and a half of regular football at The Recreation Ground, scoring 8 times in 57 appearances before joining Southern League Bedford Town as player/assistant manager in May 1951, where over the next three years he was a regular in the side and showed good goalscoring form, scoring 62 goals in 149 appearances for the club. He departed in 1954 and saw out his career with a spell at Eastern Counties League side Biggleswade Town. Woodward had a coaching spell at South Midlands League side Potton United.