It would be better to give the whole truth rather than try and land it on Churchill individually, quoting
one suspect author as only source.
1. The UK had a coalition government and a war cabinet of 9 not a Churchillian dictatorship, so blaming it on Churchill is pure hyperbole.
2. Burma fell in 42 from which point Bengal lost previous regular rice imports and was now on the front line with the Japanese. Had Japan reached Bengal the death figures would have been an order of magnitude higher. To hugely understate it, Japan didn't have a great reputation for treatment of populations of countries they occupied. Burma was the location of the infamous Burma-Siam railway that was being built with slave labour, to supply Burma and the expected Bengal front.
3. Many of the Indian states under their respective Maharajas applied trade restrictions with Bengal after the fall of Burma, through 42 starting with Punjab. That significantly heightened food shortages and profiteering. Seeing how prices rose most of the other Indian states joined in. It was the inability to internally import rice that was perhaps the largest single factor. Thanks to the vassal nature of the states under the Raj these decisions were not by the British.
4. Bengal was inundated with half a million refugees fleeing Burma, and thousands more defeated troops. Most were injured and ill.
5. At that point in the war there was little could be done to prevent Japanese attacks in the Bay of Bengal. The War Cabinet did indeed decline Mountbatten's requests for shipping food due to expected shipping losses. The cabinet papers are now freely available.
6. A series of natural disasters in the region, including extensive crop disease, a cyclone that killed 15,000 and spread the disease spores widely, followed by further floods. What was Churchill's part in these?
Churchill had faults, and some appalling decisions in his career that could be easily criticised. The Bengal famine is probably one of the weakest as it is mostly untrue.