Dover was born in Calcutta to Eurasian parents in 1904. Dover's mixed-race ancestry (English father, Indian mother) and his studies in biology fostered in him a strong concern with ethnic minorities and their exclusion and oppression, as well as their cultural achievements. He studied at St Joseph's College, Calcutta, and Medical College, Calcutta, before joining the Zoological Survey of India as a temporary assistant in charge of entomology, also helping with an anthropometric study of the Eurasian community of Calcutta, writing several scientific articles and editing the Eurasian magazine New Outlook. In 1929 he met Jawaharlal Nehru. After a brief time studying at the University of Edinburgh (zoology and botany) and at the Natural History Museum in London (systematic entomology), he took up various zoological posts in Malaya and India where he also applied his scientific expertise to social welfare problems. 

Dover settled in London in 1934 in order to further pursue anthropological studies on issues of race. Julian Huxley supplied Dover with an early proof copy of We Europeans. This book marked the turning point for Dover's thinking on issues of race and drove him to write Half-Caste. He travelled widely in Europe, lecturing on race and using his scientific knowledge to help dispel the eugenicist myths surrounding race and in particular mixed-race lineage. In Britain Dover also wrote several papers and books about race including Half-Caste and Hell in the Sunshine. He was a firm believer in Indian independence, describing himself as the first Eurasian to ally himself with the struggle for Indian independence. Through these nationalist sympathies he became loosely linked with Krishna Menon and the India League. 

In the 1940s he was a regular contributor to the BBC Indian Section of the Eastern Service alongside many other Britain-based South Asians such as Mulk Raj Anand, M. J. Tambimuttu and Venu Chitale. He also befriended George Orwell. During the Second World War, he worked in Civil Defence and served with the Royal Army Ordnance Corps. He also found work as a lecturer for the Ministry of Information and edited Three, the journal of No. Three Army Formation College. Furthermore, Dover developed a mosquito repellent, known as 'Dover's Cream', which was widely used by soldiers serving in South and South East Asia. 

In 1947, after the war, Dover moved to the United States where he held a range of visiting academic posts in the field of anthropology and 'inter-group relations', focusing his concern on American minority communities.  His interests extended into the field of visual art, including 'Negro' arts. He was a member of the Faculty of Fisk University, as Visiting Lecturer in Anthropology. He also briefly lectured at the New School of Social Research, New York, and Howard University. During this period, Dover renewed his interest in African American culture. In the 1950s, after the Second World War and his career in the USA, he returned to London. He continued to lecture and contribute to publications on minority issues and culture until his death.