Born in Glasgow, Grogan and her two sisters all attended the Notre Dame Convent School. Aged 17 while within the Pollok Inn, a public house in Glasgow, she was a bystander when a fight broke out between several patrons. A broken bottle was hurled in her direction as she was fleeing, and she was left severely injured with a prominent scar on the left side of her face. Grogan states that her parents still find it hard to read about the incident. She began filming Gregory's Girl just three months after the incident.