Early life and education
Williams was born in Great Britain in a Welsh family with musical influences. She began private lessons at age five and was able to read music before she reading English. Her formal training started with five years at the Royal Academy of Music where she specialized in the organ, performing as a student of David Sanger. She obtained the Academy's prestigious Recital Diploma, together with the LRAM for both organ and piano. She was awarded all the major prizes for organ performing and, during her studies, she became a Fellow of the Royal College of Organists and a Fellow of Trinity College London, as well as an Associate of the Royal College of Music.
Williams has also studied with Daniel Roth, the Organist at the Church of St. Sulpice, Paris. Moving to the United States, Williams undertook postgraduate study at Yale University  under the direction of Thomas Murray. She was appointed University Chapel Organist and was awarded an Artist Diploma (AD) together with the Charles Ives Prize for outstanding achievement. She then relocated to New York City where she became the Associate Organist at the Cathedral of the Incarnation in Long Island's Garden City. She undertook doctoral study under McNeil Robinson at the Manhattan School of Music, where she received the Helen Cohn award for her Doctor of Musical Arts (D.M.A.) degree.