Peters, the son of a London doctor, was educated at Cambridge University and St. Bartholomew's Hospital, London. After teaching briefly in Cambridge, he accepted the Whitley Chair of Biochemistry at Oxford, which he held from 1923 until his retirement in 1954.

Between 1928 and 1935 Peters and his Oxford colleagues succeeded in showing for the first time the precise activity of a vitamin in the body. Working with vitamin B₁, or thiamine – the antiberiberi factor first described by Christiaan Eijkman – they fed pigeons on a diet of polished rice. This was free of thiamine and produced a number of debilitating symptoms in most of the birds. As one of these symptoms was convulsions, Peters suspected that the thiamine deficiency could involve the central nervous system. He consequently began a search of the pigeon's brain for what he termed a ‘biochemical lesion’.

The first hint of the role of thiamine was provided by the failure of minced pigeon brain to take up as much oxygen as the brain of a normally fed bird. The lesion was promptly reversed by the addition of thiamine. Further work showed an accumulation of lactic acid in the pigeon brain. As this is one of the intermediate products in the metabolism of carbohydrates into carbon dioxide and water it seemed clear that thiamine must be an essential ingredient in this metabolic pathway.

Peters's work therefore provided the first proof of the action of any vitamin upon an enzyme system in vitro.