In 1938, she began her medical training at Tite Street Children's Hospital, in Chelsea. After the Second World War broke out, she worked as a theatre assistant and, in 1943, began her training to join the Queen Alexandra's Royal Naval Nursing Service at Royal Naval Hospital, Haslar. She worked there until 1944, and before the Normandy landings she recalled cycling to the hospital past columns of Canadian tanks, to calls of "Hello sugar! Are you rationed?" from the male soldiers. By the end of 1944, she had transferred to Australia, travelling there on a troopship with 4,000 Royal Marines. In 1945, Cooke volunteered to move from her nursing post at Royal Naval Hospital, Herne Bay, in Sydney, to assist the medical team aboard. The ship's first mission was to collect 1,000 Australian former prisoners of war from Manila. The embarkation alone took three days, and Cooke spent some of her time assisting in the creation of a body-length plaster case, complete with stretcher poles, to move a man who was suffering from spinal tuberculosis. Shortly afterwards, on 24 October, the ship sailed for Papua New Guinea to assist 1,254 Punjabi soldiers suffering from malaria and eczema. Cooke warned the soldiers that the methylated spirits used to clean ulcers would hurt; her words were translated as "If doesn't hurt, it doesn't do any good." Rev H. Kennen, who was also aboard Formidable, recalled that during the ship's line-crossing ceremony Cooke "did fail to perform the deep and graceful traditional curtsy due, thereby insulting the First Lord of the Admiralty", and was punished "as a point of principle" with "ducking in an improvised pool". After her work aboard Formidable, she transferred to to travel back to United Kingdom. After the war, Cooke served at RNAS Dale, with a young David Attenborough, who was performing National Service at the time. She was appointed an Associate of the Royal Red Cross in the 1954 New Year Honours, and advanced to a Member of the Royal Red Cross in the 1969 Birthday Honours. She then served in Chatham, Hong Kong, Malta and Plymouth, before becoming the lead tutor at the Royal Navy training school in 1970, and finally becoming Matron-in-Chief of the QARNNS in 1973. She was appointed a Commander of the Order of St John in 1974, and a Commander of the Order of the British Empire in the 1975 Birthday Honours.
