After failing the Irish Intermediate Certificate he left school to pursue an apprenticeship in painting and decorating, taking his Junior and Senior Irish Trade Certificates, and the City and Guilds of London exams at the Dublin Institute of Technology, Bolton Street.
Murphy's last play, with an all-female cast, The Hen Night Epiphany, premiered at The Focus Theatre, Dublin in September 2011 and was published by Oberon Books.
In May 2017 Murphy's second Verbatim piece for the Abbey, looking at police corruption, "A Whisper Anywhere Else", was produced at the Peacock Theatre.
His first Verbatim play for the Abbey, "Of This Brave Time", commissioned to commemorate the 1916 Easter Rising, toured the UK in 2016 and later returned to the Peacock stage for a short run.
A new full-length play, commissioned to mark the centenary of the drawing of the Irish border "The Cartographer's Pen, opened at the Town Hall Theatre, Cavan, in May 2022.