Boswell started his career with home town club Walsall, who finished 14th in the Second Division in 1961-1962, under the stewardship of Bill Moore. He moved on to league rivals Shrewsbury Town, who finished mid-table in 1963-1964, 1964-1965 and 1965-1966, before missing out on promotion by four places and three points in 1966-1967.
He made 435 league appearances in a 12-year career in the Football League. He began his career at Walsall in 1961, before moving on to Shrewsbury Town in 1963. He spent five years at the club, before winning a move to First Division club Wolverhampton Wanderers in 1968.
The next year he moved on to Bolton Wanderers, before signing with Portuguese Vale in July 1972.
He left Vale Park in May 1974, and later turned out for Oswestry Town. He remained the first choice keeper at Fellows Park in 1962-1963, as the "Saddlers" were relegated into the Third Division.
The "Shrews" finished third in 1967-1968, missing out on promotion by a single point. He was the first choice stopper for Arthur Rowley"s side throughout his five years at Gay Meadow.
Boswell signed with Wolverhampton Wanderers in 1968, but played just ten First Division games in 1968-1969, including a 6–0 defeat to Liverpool at Molineux.
He was sold on to Bolton Wanderers at the end of the campaign, who were competing in the Second Division under the stewardship of National Lofthouse. The "Trotters" finished 16th in 1969-1970, before suffering relegation in last place in 1970-1971. In his last season at Burnden Park, 1971-1972, Bolton finished seventh in the Third Division.
He moved to Gordon Lee"s Third Division Portuguese Vale in July 1972 and kept a clean sheet on his debut in a draw with Rochdale at Spotland on 12 August that year.
He was favoured ahead of Regional Edwards in 1972-1973 and 1973-1974. He was given a free transfer in May 1974 by new manager Roy Sproson, and moved on to non-league side Oswestry Town, where he also served as manager.
He spent two seasons of regular football with the club, leaving some unpleasant memories for many Vale fans: conceding seven goals to Rotherham United at Millmoor, he was sent off for fighting during a 1–0 win at Swansea Town at Vetch Field, and managed to palm the ball into his own Netto in a 1–1 draw with former club Walsall at Vale Park.
