Born in Gillingham, Kent, Kedwell came through the youth system of Kent-based Chatham Town and played one season for the club before joining Tonbridge Angelsin the summer of 2002. His spell at the Longmead Stadium was short-lived when in October 2002 he signed for Fisher Athletic and stayed with the side until January 2003. He had a short spell at Lordswood before joining Maidstone United in the summer of 2003, staying until the end of the following season. Kedwell then signed for Kent League side Herne Bay where he was the top scorer that season finishing with 28 goals in all competitions. This attracted the attention of ConferenceSouth sideWelling United, who signed the striker in the summer. Kedwell enjoyed two seasons at Welling, scoring 38 league goals, and made a further step up in 2007 when he signed for Conference side Grays Athletic for £12,000, a club record. He spent one full season at the Essex club scoring 13 league goals, and at the end of the season he dropped down a division when he signed for AFC Wimbledon for £10,000. Whilst at the south-west London club, Kedwell found some of the best scoring form of his career, and scored 67 goals in three seasons.
League
Kedwell scored the winning penalty in the 2011 Conference Premier play-off Finalpenalty shoot-out against Luton Town to send AFC Wimbledon into the Football League. On 1 July 2011, he signed for League Two side Gillingham, his hometown club, for a fee of £60,000. He made his league debut for Gillingham on 6 August in a 1–0 win over Cheltenham Town at Priestfield Stadium. He finished his first season with the Gills as the club's top scorer with a total of 14 goals, 12 of which came in the league. Kedwell was made captain of Gillingham for their first competitive game of the 2012–13 season in the League Cup against Bristol City. He began the league campaign in with eight goals in the Gills' first ten league matches. Kedwell also managed to score the goal that secured promotion in a 1–0 home victory over Torquay United. He finished the season once again as the club's top goal scorer, scoring 16 goals in all competitions, 14 of which helped the Gills to win the League Two championship. On 12 May 2014, Kedwell signed a new two-year deal with the "Gills".
Kedwell joined Havant & Waterlooville for the 2019–20 season, scoring 11 goals in 25 league appearances before the season was halted in March due to the COVID-19 pandemic. He was released as a free agent in July 2020.
