Grinham is an Olympic gold medallist, Commonwealth and European champion, and former world record-holder.

[5] Grinham competed in the 1956 Olympic Games in Melbourne, Australia, winning the 100-metre backstroke, setting a world record of 1:12.9.

[1] Grinham competed in the 1958 British Empire and Commonwealth Games in Cardiff, Wales, and won the 100-metre backstroke in 1:11.9.

She became the first woman in any sport to hold Olympic, Commonwealth and European gold medals at the same time.

[2] In 2007 she was appointed a Member of the Order of the British Empire (MBE) in the Queen's Birthday Honours list, 50 years after winning gold in Melbourne.