Lincoln was born in London to a South African nurse mother and a British civil engineer father. He grew up in Hull and moved to Bath at the age of ten. After leaving Beechen Cliff School, he attended the Royal Academy of Dramatic Arts (RADA), where he changed his name from Clutterbuck to Lincoln. He made his first on-screen appearance in an episode of Drop the Dead Donkey. His brother is Richard Clutterbuck who works as deputy headteacher at St Laurence School in Bradford on Avon.