Churchill had little to do with it, other than not having enough shipping and having to prioritise feeding troops who were fighting Nazis at the time.

Also from your link...

The provincial government never formally declared a state of famine, and its humanitarian aid was ineffective through the worst months of the crisis. It attempted to fix the price of rice paddy through price controls which resulted in a black market which encouraged sellers to withhold stocks, leading to hyperinflation from speculation and hoarding after controls were abandoned. Aid increased significantly when the British Indian Army took control of funding in October 1943