Grant's father was trained at Sandhurst, Berkshire and served with the Seaforth Highlanders for eight years in Malaya, Germany and Scotland. He ran a carpet firm, pursued hobbies such as golf and painting watercolours, and raised his family in Chiswick, west London, where the Grants lived next to Arlington Park Mansions on Sutton Lane. His mother worked as a schoolteacher and taught Latin, French and music for more than 30 years in the state schools of west London. She died at the age of 65, 18 months after being diagnosed with pancreatic cancer.