Brasher (then known as Shirley Bloomer) won the singles title at the 1957 French Championships, defeating Dorothy Head Knode in the final in straight sets.

[3] Bloomer teamed with Darlene Hard to win the women's doubles title at the 1957 French Championships, defeating Yola Ramírez and Rosie Reyes in the final 7–5, 4–6, 7–5.

She teamed with Nicola Pietrangeli to win the mixed doubles title at the 1958 French Championships, defeating Lorraine Coghlan and Robert Howe in the final.

In 1960, she and Christine Truman won the final doubles match against Janet Hopps and Dorothy Knode to bring her team to another 4–3 victory over the U.S. Bloomer played a hard baseline game, and her tennis was concerted rather than spectacular.

In April 1959, she married Olympic champion athlete Chris Brasher who helped pace Roger Bannister to running the first sub-four-minute mile in 1954.