Marrack was born in Clevedon in Somerset and educated at Blundell's School in Tiverton, St John's College, Cambridge, and at the London Hospital Medical College.
Marrack served in the RAMC from 1914 to 1919 and was appointed Medical Officer on Poison Gas to the British Army.
He received the Distinguished Service Award of the First International Congress of Immunology in 1971.
His citation for this award reads: "For revolutionary ideas that have become commonplace in his lifetime, and for pioneering in the physico-chemical interpretation of antigen-antibody interactions".
He was adviser to the Ministry of Food during the Second World War and was instrumental in developing Great Britain's nutrition policy and accurately forecasting the country's post-war nutritional needs.