Originally from Worcester, Narraway attended the Kings School and joined Gloucester straight out of school, going on to make his full debut in 2003 against Leeds. Narraway established himself as a powerful and dynamic ball carrier at no.8 and earned himself an international call up in 2008 when he lined up at Twickenham against Wales and went on to earn seven caps in total.
Long presumed to be a one club man, Narraway moved onto pastures new with Perpignan in 2012. After a two-year spell in France with Perpignan, Narraway returned to England with London Irish for the 2014/15 season.
After a chain of impressive performances, he was appointed captain of Premiership side London Irish ahead of their 2016/17 campaign, taking over from George Skivington, who called time on his playing career at the end of the 2015 season.
On 12 April 2017 it was announced that Luke had signed a two-year contract to become a player- coach at Coventry. They went on to win National League 1 in Narraway's first year, achieving promotion to the RFU Championship.
Narraway spent a year working with the Bordeaux-Begles before joining Dragons in 2019 as head coach for their Celtic Cup team before joining the senior coaching staff permanently as forwards coach ahead of the 2020/2021 season.