Born in London, William Woolf Mushin was educated at the Davenant Foundation School, and then the London Hospital, qualifying in 1933. He was appointed to the Eastman Dental Clinic and then became first assistant to Robert Macintosh at Oxford University. In 1947 he moved to the Welsh National School of Medicine to establish a new department of anaesthetics, largely because of concerns expressed by the Cardiff coroner over the contribution of anaesthesia to surgical deaths. He suggested changes in training and emphasised the need for research as well as leading a national study on post-operative deaths that later became the National Confidential Enquiry Into Perioperative Deaths.

Mushin believed in the importance of basic sciences in anaesthesia, appointing a physicist and physiologist to his department and co-authoring Physics for the Anaesthetist with Robert Macintosh in 1946. He advocated the involvement of anaesthetists in intensive care and was a pioneer in the treatment of chronic pain. He was a founder member of the Pain Society who elected him life president in recognition.

Mushin played a major role in transforming anaesthesia into a scientific specialty and, shortly before his death aged 82, the Royal College of Anaesthetists was granted a charter.