Kroto was born in Wisbech, Isle of Ely, Cambridgeshire, England, to Edith and Heinz Krotoschiner, his name being of Silesian origin. His fathers family came from Bojanowo, Poland, and his mothers from Berlin. Both of his parents were born in Berlin and fled to Great Britain in the 1930s as refugees from Nazi Germany; his father was Jewish. Harry was raised in Bolton while the British authorities interned his father on the Isle of Man as an enemy alien during World War II. Kroto attended Bolton School, where he was a contemporary of the actor Ian McKellen. In 1955, Harold's father shortened the family name to Kroto.
As a child, he became fascinated by a Meccano set. Kroto credited Meccano, as well as his aiding his father in the latter's balloon factory after World War II – amongst other things – with developing skills useful in scientific research. He developed an interest in chemistry, physics, and mathematics in secondary school, and because his sixth form chemistry teacher (Harry Heaney – who subsequently became a university professor) felt that the University of Sheffield had the best chemistry department in the United Kingdom, he went to Sheffield.
Although raised Jewish, Kroto stated that religion never made any sense to him. He was a humanist who claimed to have three religions: Amnesty Internationalism, atheism, and humour. He was a distinguished supporter of the British Humanist Association. In 2003 he was one of 22 Nobel Laureates who signed the Humanist Manifesto.
In 2015, Kroto signed the Mainau Declaration 2015 on Climate Change on the final day of the 65th Lindau Nobel Laureate Meeting. The declaration was signed by a total of 76 Nobel Laureates and handed to then-President of the French Republic, François Hollande, as part of the successful COP21 climate summit in Paris.