Which 1943 famine in British India killed some three million during a food-exporting year?

The Bengal famine. Rice supply was disrupted by the fall of Burma, by a cyclone, by a denial policy that removed boats and stocks from coastal districts to deny them to an expected Japanese invasion, and by provincial governments blocking grain movement between them.

Amartya Sen used it to make a general argument that changed famine economics: there was no dramatic shortfall in food available in Bengal that year. What collapsed was entitlement - wartime inflation and speculation put rice beyond the reach of rural labourers whose wages did not move, so people starved in a province with food in it, sold at a price they could not pay. His conclusion, that famines do not occur in functioning democracies with a free press, follows from the same analysis.

Churchill's role is argued about and the argument is often conducted badly. Requests for shipping and grain imports were repeatedly refused or reduced, with wartime shipping priorities given as the reason, and his recorded remarks about Indians are contemptuous; against that, the war's demands on shipping were real and the provincial administration's failures were substantial. That the response was inadequate is not in dispute; whether it amounted to deliberate policy is.