https://en.wikipedia.org/wiki/Bengal_famine_of_1943
I keep being surprised how true it is that the victors get to write the history books. Churchill killed a third as many people as Hitler did but people generally seem to be OK with that.
1. The UK had a coalition government and a war cabinet of 9 not a dictatorship by Churchill, so "directly responsible" 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.
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. It was the inability to internally import rice that was perhaps the largest single factor.
4. Bengal was inundated with half a million refugees fleeing Burma.
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 losses.
6. A series of natural disasters in the region, including extensive crop disease and a cyclone that killed 15,000 and spread the disease spores widely.
Churchill personally could have prevented all that, at the height of the war?
Now had you pointed at Bengal's governor, who made some questionable decisions during the crisis, I think you'd have had more of a case.