Fox (originally Fuchs), the son of an officer in the Prussian army, was born in London and educated at Cambridge University; after war service, he served as a fellow from 1920 to 1928. He then moved to Birmingham as professor of zoology, a post he held until 1941 when he accepted a similar chair at Bedford College, London, where he remained until his retirement in 1954.

Fox, a zoologist of wide interests, is best known for his work on invertebrate blood pigments. In 1871 Ray Lankester had noted that the red blood of the water flea Daphnia, a crustacean, was due to the presence of the pigment hemoglobin. Other crustaceans, such as lobsters, were blue-blooded with the pigment hemocyanin in their blood.

It had been observed that the transparent Daphnia could become redder or paler by synthesizing or breaking down blood hemoglobin. This was done at a rate far in excess of that noted in any other creature. Fox showed by laboratory experiments in the 1940s that the response was controlled by the level of dissolved oxygen in the water. If this were low, hemoglobin, with its affinity for oxygen, was synthesized; if high, Daphnia lose their hemoglobin and become colorless.

Earlier, in 1923, Fox had repeated the controversial experiments of Paul Kammerer on the supposed elongations produced in the siphons of the sea squirt Ciona intestinalis. He reported that in none of the operated animals was there any further growth of the siphons once the original length had been attained, and went on to suggest that Kammerer's results could have been produced by keeping the animals in a highly nutritious solution, an explanation Kammerer was quick to dismiss.