Grant considered himself to have been partly Jewish.
Grant was born Archibald Alec Leach on January 18, 1904 at 15 Hughenden Road in the northern Bristol suburb of Horfield. He was the second child of Elias James Leach (1873–1935) and Elsie Maria Leach (née Kingdon; 1877–1973). Elias worked as a tailor's presser at a clothes factory while Elsie worked as a seamstress. Grant's elder brother, John William Elias Leach (1899–1900), died of tuberculous meningitis. He had an unhappy upbringing; his father was an alcoholic, and his mother suffered from clinical depression. He had a traumatic childhood, it was horrible.
Grant's biographer Graham McCann mentions that Maureen Donaldson, a lover of Grant in the 1970s, claimed in her book that his mother "did not know how to give affection and did not know how to receive it either." Another biographer, Geoffrey Wansell, notes that Elsie blamed herself bitterly for the death of Grant's older brother John, and never recovered from it. Grant later acknowledged that his negative experiences with his fiercely independent mother affected his relationships with women later in life. She frowned on alcohol and tobacco, and would reduce pocket money for minor mishaps. Grant later attributed her behaviour towards him as down to her being overprotective, fearing that she would lose him as she did John.
When Grant was nine years old, his father placed his mother in Glenside Hospital (a mental institution), and told him that she had gone away on a "long holiday", later declaring that she had died. Grant grew up resenting his mother, particularly after she left the family. After Elsie was gone, Grant and his father moved into the home of his grandmother in Bristol. When Grant was 10, his father remarried and started a new family that did not include his son. Grant did not learn that his mother was still alive until he was 31, when his father confessed to the lie, shortly before his own death. Grant made arrangements for his mother to leave the institution in June 1935, shortly after he learned of her whereabouts. He visited her during a break to England in October 1938, after filming for Gunga Din was completed.
Due to alienation from his parents, he found it difficult to socialize and had a nervous disposition. He enjoyed the theatre, particularly pantomimes at Christmas which he would attend with his father.