Constable started his career with the Cirencester Town youth system, before breaking into the first team during the 2002–03 season. He moved to Chippenham Town in 2003, before signing for Walsall in the Football League in 2005. He moved out on loan to Kidderminster Harriers of the Conference National in 2006, before signing permanently in 2007. After a year at the club, during which he scored the first club goal at the new Wembley Stadium in the 2007 FA Trophy Final, he returned to the League with Shrewsbury Town. After spending 2008–09 on loan at Oxford United, he signed for the club permanently in 2009. Constable scored the second goal in Oxford's 3–1 2010 Conference Premier play-off Final victory over York City in 2010, which secured Oxford's promotion into League Two. He was leading goalscorer in each of his six seasons at the club, and when he left after 2013–14 he had scored 106 goals, one short of the club record.