Murray earned his first call-up to the Great Britain men's national basketball team in 2013. He has since featured in all of Great Britain's major tournaments and qualifying campaigns including FIBA Eurobasket 2013 and FIBA Eurobasket 2017. During that time, Murray has established a reputation as one of the National Team's finest marksmen with a national team career three-point field goal percentage of 0.407 (55/135) as of 24 February 2020.