Janet Morgan was in 1948 and 1949, twice in the final of the British Open, which was considered at the time as the unofficial world championship. They lost both games against her compatriot Joan Curry. In 1950 she finally won her first title when she defeated smooth curry in three sets. This track defended consistently until 1959, which they won the tournament a total of ten times. Only Heather McKay could often win the British Open with 16 titles. Due to ongoing back injury she had to end her active career as a player in 1960. She was inducted into the World Squash Hall of Fame in 1983, the first president of the Women's International Squash Players Association and in 1993 posthumously.
Janet Morgan was also active in tennis. Between 1946 and 1955 she participated in the tournament every year at Wimbledon and in 1946 was part of the British team at the Wightman Cup.