You can find it spelt both ways on the internet.
John Radcliffe (1650 – 1 November 1714) was an English physician, academic, and politician. He was a prominent figure in Oxford, and a number of landmark buildings in the city were named after him, including the Radcliffe Camera, Radcliffe Infirmary, Radcliffe Science Library, Radcliffe Primary Care, and the Radcliffe Observatory.
He was a respected physician and academic, and his legacy continues to be felt in Oxford University and the surrounding community.
Just what the doctor ordered.