He won seventeen caps for his country, helping the Scotland national team to qualify for the 1958 FIFA World Cup.

Starting his career with Blackpool in 1947, he went on to spend the next fourteen years with the club, helping them to the FA Cup final in 1951 and 1953, the latter of which ended in victory for the Tangerines.

In 1952–53, Blackpool bounced back from their disappointment in 1951's FA Cup final when Mudie's last-minute goal against Tottenham Hotspur in that season's semi-final sealed a return to Wembley, this time to face Bolton Wanderers.

[3] This match is widely remembered as the "Matthews final", due to the winger helping to turn a 3–1 deficit into a 4–3 win for Blackpool.

[3] This change of position, combined with his scoring 22 and 38 goals in consecutive seasons, enabled him to achieve international recognition.

[6] To address the situation manager Tony Waddington brought back Stanley Matthews to the club and it had the desired effect with 35,974 attending the next match against Huddersfield Town.

[6] Mudie moved to Stoke's local rivals Port Vale in November 1963 along with Ron Wilson in a "package" deal of between £12,000 and £15,000.

[8] After Freddie Steele's departure, Mudie became player-manager in February 1965, combining for a third time with boyhood Vale supporter Matthews, who became the Valiants' general-manager a few months later after playing his final First Division match for Stoke against Fulham five days after his 50th birthday.

[8] After his playing retirement, Mudie lived in Stoke-on-Trent, his adopted hometown, setting up a painting and decorating business.