Dawes played club rugby for Newbridge in Monmouthshire. He then joined London Welsh. Dawes was appointed captain, and effectively also as coach, for the 1965-66 season, leading the club in a period of great success in the late 1960s. He initially significantly increased fitness levels, and then led the club in an open, running, quick-passing, attacking style of rugby, including an overlapping full-back, and relatively skilled forwards. One 1968-69 performance was described by journalist John Reason as "one of the most brilliant exhibitions of club football it has been my privilege to see," and by journalist Terry O'Connor as "the finest display by a club team I can remember', further describing London Welsh 'switching attacks with speed and handling skill.'
International
Dawes won his first cap for Wales against Ireland in 1964. He was selected for Wales' first overseas tour later the same year and played in the Welsh rugby team's first match outside of Europe and its first in the Southern Hemisphere. He played against East Africa in Nairobi on 12 May 1964, Wales winning 26-8. He went on to make 22 appearances for Wales, captaining the side in six of them, including leading the Grand Slam winning side of 1971.
In 1971, Dawes was appointed captain of the British and Irish Lions side for the tour to New Zealand. This side, coached by Carwyn James, became the first and so far the only Lions team to win a series in New Zealand. Dawes was also captain of the Barbarians side that beat New Zealand in Cardiff in 1973. Today he holds a proud record for any Welshman in the fact that as a player or coach he has never lost to an England side. He is one of five captains to lead his side to a test series win on New Zealand soil, along with Philip J. Nel, Trevor Allan, Andrew Slack and Philippe Saint-André.
Rugby coaching career
After retiring as a player, Dawes became coach of the Welsh national side in 1974, a post he held until 1979. This was one of the most successful periods in the history of Welsh rugby, with the team winning the Five Nations Championship four times in the five seasons between 1975 and 1979, including two Grand Slams. He also coached the 1977 British Lions tour to New Zealand, but was unable to repeat the success of 1971. Ian McGeechan has said of this tour "perhaps John, a natural player and leader in his time, was just not so good at putting things across," but others have pointed out that the 1977 Lions nearly drew the series, and that subsequent Lions tours to New Zealand fared much worse.