Grant was born at Charing Cross Hospital in Hammersmith, London, the second son of Fynvola Susan MacLean (b. Wickham, Hampshire, 11 October 1933; d. Hounslow, London, July 2001) and Captain James Murray Grant (b. 1929). Grant's grandfather, Colonel James Murray Grant, DSO was decorated for bravery and leadership at Saint-Valery-en-Caux during World War II. Genealogist Antony Adolph has described Grant's family history as "a colourful Anglo-Scottish tapestry of warriors, empire-builders and aristocracy." A few of his notable ancestors include William Drummond, 4th Viscount Strathallan, Dr. James Stewart, John Murray, 1st Marquess of Atholl, Heneage Finch, 1st Earl of Nottingham, Sir Evan Nepean, and a sister of former Prime Minister Spencer Perceval.
Grant's father was an officer in the Seaforth Highlanders for eight years in Malaya and Germany. 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. In September 2006, a collection of Capt. Grant's paintings was hosted by the John Martin Gallery in a charity exhibition, organised by his son, called "James Grant: 30 Years of Watercolours." 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 67, 18 months after being diagnosed with pancreatic cancer.
Grant's accent is an inheritance from his mother; and, on Inside the Actors Studio in 2002, he credited her with "any acting genes that [he] might have." Both his parents were children of military families, but, despite his parents' backgrounds, Grant has stated that his family was not always affluent while he was growing up. Grant spent his childhood summers shooting and hunting with his grandfather in Scotland. Grant has an older brother, James, living in Portugal.
Grant started his education at Hogarth Primary School in Chiswick but then moved to St Peter's Primary School in Hammersmith, Grant was then educated at an independent prep school Wetherby School. From 1969 to 1978, he attended the independent Latymer Upper School in Hammersmith on a scholarship and played 1st XV rugby, cricket and football for the school. He also represented Latymer on the popular quiz show, Top of the Form, an academic competition between two teams of four secondary school students each.
In 1979, Grant won the Galsworthy scholarship to New College, Oxford, where he starred in his first film, Privileged, produced by the Oxford University Film Foundation. He read English and graduated with 2:1 honours. Actress Anna Chancellor, who met Grant while she was still at university, has recalled, "I first met Hugh at a party at Oxford. There was something magical about him. He was a star even then, without having done anything. Grant joined the exclusive Piers Gaveston Society at Oxford, a group with a reputation for debauchery and decadence".
Grant received an offer from the Courtauld Institute of Art, University of London to pursue a PhD in the history of art, but decided not to take the offer because he failed to secure a grant. Viewing acting as nothing more than a creative outlet, he joined the Oxford University Dramatic Society and starred in a successful touring production of Twelfth Night.
After making his debut as Hughie Grant in the Oxford-financed Privileged (1982), Grant dabbled in a variety of jobs, such as working as an assistant groundsman at Fulham Football Club, tutoring, writing comedy sketches for TV shows, and working for Talkback Productions to write and produce radio commercials for products such as Mighty White bread and Red Stripe lager. To obtain his Equity card, he joined the Nottingham Playhouse, a regional theatre, and lived for a year at Park Terrace in The Park Estate. Bored with small acting parts, he created his own comedy revue called The Jockeys of Norfolk, a name taken from Shakespeare's Richard III, with friends Chris Lang and Andy Taylor. The group toured London's pub comedy circuit with stops at The George IV in Chiswick, Canal Cafe Theatre in Little Venice and The King's Head in Islington. Starting on a low note, The Jockeys of Norfolk eventually proved a hit at the Edinburgh Festival after their sketch on the Nativity, told as an Ealing comedy, gained them a spot on the BBC2 TV show called Edinburgh Nights. During this time, Grant also appeared in theatre productions of plays such as An Inspector Calls (at the Royal Exchange, Manchester), Lady Windermere's Fan, and Coriolanus.