City had to wait until November 1947 and his RAF demob to sign Dawson as a full-time professional with the club.
The Scot made his debut in September 1946, however, at home against Birmingham City but he made only five league appearances for the Foxes during his time in Leicestershire.
His senior appearances in a City shirt were brief, but his qualities on the wing caught the attention of League champions Portsmouth, who signed him in June 1949. He was primarily back-up on the south coast though, with England wingers Jack Froggatt and Peter Harris the main men out wide for Portsmouth. He made just one appearance as Pompey won the league again that year.
He moved on to play for Corby Town, Brush Sports and Hinckley Athletic.