John Brockway won the first of his seven Amateur Swimming Association British national titles at 100y/110y backstroke in 1948, the same year he reached the final of the metric equivalent of that event at the London Olympic Games. His first major international medal came at the 1950 British Empire Games where he placed second behind South Africa's Jackie Wiid and it was the next celebration of these Games that was to be the highlight of his career. In Vancouver in 1954 at the newly renamed British Empire & Commonwealth Games he held off the challenge of Lincoln Hurring to become the first representative of Wales to win a gold medal in swimming at any Empire Games.
He narrowly failed to make a second Olympic final in 1952 but won a bronze medal at the 1954 European Championships in Torino. Brockway was captain of the British swimming on his third Olympic appearance at Melbourne and continued to swim at the highest level until 1958. His last international event was in 1958 at the British Empire & Commonwealth Games where he took the competitors oath and swam in the finals of both the 110y backstroke and the medley relay (with the non-Olympians B.F. Newman, J.E. Beaven, and R. Evans) - finishing sixth both times. In addition to his ASA titles Brockway was Welsh backstroke champion eight times during his career. Outside the swimming pool he, who was a qualified engineer, spent his working life in the steel industry.