Miss Elwell earned a bachelor's degree in biological sciences from Columbia College, Columbia University, New York, in 1994. She completed her medical school training at the University of Cambridge, from which she earned a Master of Arts degree in 2004, and the Imperial College School of Medicine, London, from which she earned bachelor's degrees in medicine and surgery. She completed her neurosurgical training on the North Thames Neurosurgical London Rotation, followed by specialist training in complex spinal surgery as a Central London Senior Spinal Fellow.