The following factors were responsible for famine in Bengal during British rule:

• Droughts
• Policy failures
• Government apathy

The Bengal Famine of 1943 was a man made catastrophe because under orders from British PM, WInston Churchill, the governor had to divert most of the food supply to the Indo-Burmese border in order to sustain British troops fighting against the Japanese during World War II

For further reading check the following articles:

• World War II
• Bengal Famine 1770
• European Colonialism