Well remarkably for one of these dubious factoids it does seem to be the case that about two billion people died in the undivided subcontinent during the period of British supremacy if we reckon from the battle of Plassey (1757) to partition (1947), assuming an average population of 250-260 million and an annual crude death rate averaging about 41 per thousand (around 45 in the first century, falling to 30 toward the end). But that's a very, very different matter to all deaths in the period occurring because of British rule.

Perhaps upwards of 25 million died (many of associated disease rather than starvation) in successive major famines of which mortality in the first (and possibly most severe) in Bengal in 1770 has been blamed in part on the East India Company's diversion of provincial revenues that might otherwise have funded relief operations, while the last in 1943 (again in Bengal) has been attributed partly to mobilisation of food and transport for the war against Japan. The development of communications under the Raj may have eased the spread of disease, and waterlogging-prone road and rail embankments and irrigation works have been associated with malaria, but vaccination conversely contributed to reduced smallpox deaths.

British failure to achieve earlier advance may be blamed for painfully slow population growth averaging only 0.3% and an obstinately low expectation of life at birth of under 25 years until 1920, but it seems difficult to implicate Imperial rule in more than some tens of millions of deaths - some unforeseen consequences of genuine efforts at economic improvement - and even then it remains to demonstrate conclusively that British policies were the cause of more than a fraction.

The above isn't meant to extol or even exonerate British rule: I'm far from being an admirer of the imperial venture (British or other), and the results are at best mixed (and in my opinion on balance negative, on non-demographic grounds). But it seems implausible (especially in the absence of vital indicators before the 19th century) to attribute more than a very small percentage of all deaths over the period to British actions or gratuitous omissions, and the claim of two billion victims of the Raj can be dismissed as simply absurd.

For population and mortality see Irfan Habib in Cambridge economic history of India, vol 1, ch 5, Leela & Pravin Visaria in vol 2, ch 5, and PC Mahalanobis & D Bhattacharya, Growth of population in India and Pakistan, Indian Statistical Institute, 1969. Habib offers a robust critique of British rule in Colonialization of the Indian economy, Social Scientist 3:8 (Mar 1975), but his own CEHI contribution describes Mughal India's earlier population growth as "hardly spectacular and much lower than the rate attained during the 19th century".