Originally from Hove in Sussex, England, Crocker started his working life as an apprentice to a general practitioner before going to London to attend the University College Hospital medical school.

Working as a resident medical officer with William Tilbury Fox, Crocker began a lifelong career in dermatology.

At this time, the practice of specialising in medicine was somewhat frowned upon in the United Kingdom (although more popular in continental Europe), but Tilbury Fox and Crocker were credited with bringing some structure to the field of dermatology.

[1] In 1888, Crocker published Diseases of the Skin: their Description, Pathology, Diagnosis and Treatment, a textbook that helped to establish him as a leading figure in dermatology.

[3] At a meeting of the Pathological Society of London in 1885, Crocker was the first to put forward a theory on the condition of Joseph Merrick, known as the Elephant Man.

Crocker suggested that Merrick's condition was caused by a combination of dermatolysis and bone deformities, as a result of changes in his nervous system.