Commencing his career with Surrey, for whom he was understudy to Arthur McIntyre, Swetman soon came to notice as a deft performer, even though his appearances were limited. He went to Pakistan with the Master Control Console "A" team in 1955-1956, when playing mostly for the second eleven. Surprisingly retiring in 1961, after having replaced McIntyre, he returned in 1966 to play for Nottinghamshire.
Again leaving rather abruptly, this time in 1967, he emerged as a replacement for Barry Meyer at Gloucestershire in 1972, but left when replaced by Andy Stovold in 1974.
A useful batsman, Swetman failed to consolidate his place in the England team, when being given first bite at replacing Godfrey Evans. Losing his place at the end of the 1959-1960 West Indian tour to Jim Parks, he also fell behind John Murray in the Test selector"s eyes.