Cork started off his career with Chelsea but between 2006 and 2011, he went on loan to a number of clubs, including Scunthorpe United where he was named player of the year. Without making an appearance for Chelsea, he signed permanently to Championship club Southampton in 2011 where he made over 100 appearances for them and helped them promoted to the Premier League by featuring in all their matches. Cork spent two and a half years with Premier League club Swansea City from January 2015 to July 2017 before his permanent move to Burnley where he featured in every match en route of the club qualifying to the UEFA Europa League.