Wethered and her brother Roger, who tied for the British Open title in 1921 but lost the play-off, learned the game as children. She was British Ladies' Open champion four times (1922, 1924, 1925, and 1929) and English Ladies' champion for five consecutive years (1920–24), playing undefeated for 33 matches. In addition to success in numerous mixed foursome events, she was a regular international tournament choice and played on the first Curtis Cup team in 1929, against France in 1931, and against the United States in 1932. Representing a London store, she toured the United States as a professional in 1935, winning against Babe Zaharias (Zaharias, Babe Didrikson).

In 1937 she married Sir John Heathcoat-Amory, with whom, at their home at Knightshayes Court, near Tiverton, Devon, she created a notable garden that was one of the leading British botanical collections, for which she was awarded the Royal Horticultural Society's Victoria Medal of Honour. Even after her retirement, Wethered remained an important figure in ladies' golf; she became the first president of the English Ladies' Golf Association in 1951 and was inducted into the Professional Golfers' Association (PGA) of America World Golf Hall of Fame in 1975.