> So british has nothing to do with the famine ?

You could feasibly make the argument that they exacerbated the Bengal famine. I don't think the scholarship supporting this argument is very good, but you could make the argument. As for the famines that occurred throughout the 18th and 19th centuries, no. There is no compelling reason to think that those famines occurred as a result of British mismanagement; they were the result of natural disasters.

Amartya Sen makes the argument that famines stopped occurring after India was granted independence, which alongside Churchill's general disdain for Indians is one of the more compelling reasons to think the British had anything to do with the 1943 famine, but this also coincides with the introduction of modern farming technologies (mechanization, chemical fertilizers, etc.), which complicates things.

There was also a high level of extreme poverty in India for many decades after independence. Maybe not large scale famines, but people being constantly very badly malnourished.

It also coincides with the end of WWII and thus the end of the Japanese naval threat, which was a factor in the last Bengal famine.

These correlations are hard to parse apart. There wasn't any famine in the USSR in the early 1950s either, but that does not mean that Stalin, compared to the 1930s, suddenly became a humanist leader interested in prosperity of all subjugated people.

The argument wouldn't be that the famines occurred due to british mismanagement, but rather due to british management. A country produces a certain amount of food during times of plenty. If they are careful, they will stow away some of that excess food for times of hardship. If they are being "managed" by a foreign power for its own benefit, this excess will instead be shuttled away to generate income. During times of hardship, there will be no excess to feed on and people will starve. The foreign power, in turn, will be nowhere to be found. This is no accident or failure, but rather the colony being run as intended: for profit, not for the benefit of the people living there.