Educated privately, Dudley Buxton attended University College, London, before proceeding to University College Hospital in 1878. He qualified with distinction in 1882, and achieved his MD and Membership of the Royal College of Physicians two years later.
In 1888, while anaesthetist at University College Hospital, Buxton published the work Anaesthetics: their Uses and Administration. This comprehensive volume was in print for 35 years, running to many editions and including a chapter on the medico-legal aspects of the administration of anaesthetics.
Along with Bellamy Gardner, Buxton advocated premedication in anaesthesia. For this he suggested atropine, the alkaloid of deadly nightshade, which could be used to inhibit secretions during ether anaesthesia. Later he pioneered the use of hyoscine for preoperative medication.
Among his other inventions, Buxton designed his own mouthgag and props and modified the Junker chloroform inhaler. Following his retirement due to illness in 1919, he devoted his remaining years to gardening at his home in Hertfordshire, although he continued to teach and administer anaesthetics at the West Herts Hospital almost until the day of his death.