Miller is perhaps best known for his comedy work alongside Sarah Jane Adventures star Alexander Armstrong. He also had a starring role in Primeval, as well as the first two series of Death In Paradise. He has also appeared in a number of successful British feature films, including The Parole Officer, Johnny English, and Noel Clarke's 184.108.40.206.
Miller previously began studying for a PhD in Physics, with a thesis entitled "Novel quantum effects in low-temperature quasi-zero-dimensional mesoscopic electron systems", although he later chose his comedy and acting career over completing this. He also presented an episode of the BBC's science series Horizon, entitled What Is One Degree?
He was once married to Belinda Stewart-Wilson.