Burden would eventually turn to off spin bowling following a discussion with Staples successor, Arthur Holt, about Hampshire's lack of a spin-bowler following a number of retirements.[3] He made his debut for Hampshire in first-class cricket against Worcestershire at Worcester in the 1953 County Championship, with him making a second appearance that season against Surrey.[5] He established himself in the Hampshire side following a match against Leicestershire, in which he took figures of 7 for 48.[1] He played regularly for Hampshire throughout the 1950s in partnership with fellow spinner Peter Sainsbury,[3] taking over fifty wickets in a season in 1955, 1957, and 1958.[6] He received his county cap in 1955, the same season in which he took 70 wickets at an average of 21.75.[1] Described as a genuine number eleven, he made one half century in 1960 when he came in as a nightwatchman against Warwickshire.[4] The following season, he played an important role in helping Hampshire win their first County Championship title, taking exactly fifty wickets at an average of 22.92;[6] these included his career best bowling figures of 8 for 38 against Somerset at Bournemouth.[3] However, despite a successful season, he did not feature after July, with slow left-arm orthodox spinner Alan Wassell being preferred.[3] He returned to make seventeen appearances in 1962, taking 65 wickets, albeit at a higher average of 30.38.[6] In 1963, he made just three appearances in the County Championship,[5] but did take 6 for 84 in his penultimate match against Gloucestershire.[3] He was subsequently released from his contract in August of that year to take up an appointment outside of cricket.[7] In 174 first-class matches, Burden took 481 wickets at an average of 26.11; he took 23 five wicket hauls and took ten-wickets in a match on four occasions.[8]
Burden was popular among both players and spectators and was included in a 2005 list of Hampshire cricket cult figures.[4] His obituary in Wisden declared, "The value of such a man is not to be estimated in figures."[1]Tony Lewis said of him that "his humour was never extinguished by failure" and noted that John Arlott called Burden "salt of the cricketing earth".[9] Arlott himself devoted a chapter to Burden in his book, John Arlott's Book of Cricketers.[2] Burden died suddenly at Whitchurch on 9 November 1987, aged 57.[10]