Indian historian Rudrangshu Mukherjee of Ashoka University told BBC News at Ten that Churchill was “seen as the precipitator of mass killing” because of his role in the Bengal famine of 1943.
Meanwhile, Yasmin Khan of Oxford University added on the programme that Mr Churchill was “prioritising white lives over south Asian lives” by not sending aid to India, still a British colony at that point.
The Bengal famine started after a cyclone and huge flooding in the north-western Indian region in 1942 that destroyed vital crops and infrastructure. Between two and three million people are thought to have died in the ensuing crisis.
Churchill has often been criticised for the British government not sending enough aid to the region because of a shortage of ships to transport food.
But Professor Tirthankar Roy of the London School of Economics said this was “a simplistic narrative”.
He told the Standard: “The British Indian government and the provincial government of Bengal did not take responsibility for bringing in food to the region internally, where there was no famine.
“The real question is why this didn’t happen, rather than what Churchill did.”
Historian Max Hastings, who wrote the book Winston’s War, said that it was “pretty outrageous” for the BBC not to include another voice to balance the comments of Mr Mukherjee and Ms Khan.
He told The Times: “It is entirely true, and I have described it in my own books, that Churchill behaved badly during the Bengal famine, and that is a blot on his record.
“But the BBC failed to include a voice to suggest that his services to Britain, and to mankind, were so great that they must rightfully be set in the balance against this failure. The BBC’s version was 2020 propaganda, not news or balanced history.”
Churchill was named as the “Greatest Briton” in a public poll run by the BBC in 2002. But his legacy has come under fresh scrutiny among recent anti-racist protests.
The former Prime Minister’s statue in Parliament Square was boarded up after being defaced, amid fears it could be damaged even more by protesters.
A BBC spokesperson said: “The item was the latest in a series looking at Britain’s colonial legacy worldwide.
“The series includes different perspectives from around the world, in this case from India, including a survivor from the Bengal famine, as well as Oxford historian Dr Yasmin Khan.
“The report also clearly explained Churchill’s actions in India in the context of his Second World War strategy. We believe these are all important perspectives to explore and we stand by our journalism.”