Elson was born in Leamington Spa, England. He attended Augusta State University in the U.S. and turned professional in 2003.
Elson played on the Challenge Tour in 2003, winning once at the Volvo Finnish Open. He played on the top-tier European Tour in 2004, but was unsuccessful and disappeared from both Tours for a number of years. In 2009, he made a comeback, and once again qualified for the European Tour vi Qualifying School. His second season at the highest level was more successful, with a best finish of tied for second at the Saint-Omer Open, but he still only retained partial membership for the following season. However, he started 2011 strongly, recording two top-5 finishes before matching his best ever result with a tied for second at the Madeira Islands Open. Since 2009 when Jamie started working with Scott, he has made an incredible comeback.