Murphy started out with Terry Venables' Crystal Palace, spending nine years at Selhurst Park during which time he won the FA Youth Cup in both 1977 and 1978 as part of the famous "Team of the Eighties". The club were then promoted to the First Division in Murphy's first full season in the side, but were relegated after two seasons in the top flight. However, Murphy remained with Palace winning the "Player of the Year" award in 1983.
He moved back to the top flight again, joining Chelsea on a free transfer in the summer of 1985, but his time at Stamford Bridge was plagued by lack of form and injury problems. In three seasons he made only 34 league appearances and his contract was cancelled due to injury in March 1988. He joined non-league side Fisher Athletic to finish his career.