Born in Chapel of Ease, Dawes was schooled at Lewis School, Pengam, and attended University College, Aberystwyth, then Loughborough College. A former Newbridge player, Dawes went on to play for, and captain, London Welsh. He represented Welsh Universities before winning his first cap in 1964 against Ireland.

In 1971 he was chosen as captain of the successful British Lions tour to New Zealand. Prior to the tour there were many questions raised as to whether a Welshman was the correct choice of captain on account of their reputation for insularity. However Dawes was the preferred selection of both the team manager and the coach and he had the approval and respect of all the players for his balanced approach and his superb play. He was also shrouded with compliments by his hosts for his after dinner speeches. His captaincy skills were further displayed in the famous 1973 Barbarians victory over New Zealand in Cardiff.

At the end of his playing career, after 22 caps for Wales and 4 Lions Tests, Dawes was appointed coach of the national team and in 1977 coached the British Lions on their tour to New Zealand. His services to rugby football have been rewarded with an OBE.