Grace Williams studied at Cardiff University, the Royal College of Music in London, (where her composition teacher was Vaughan Williams), and later in Vienna with Egon Wellesz. She returned to work in London, teaching and composing, from 1926 to 1946, before settling in Wales for the rest of her life.

Her Fantasia on Welsh Nursery Tunes was completed in 1940 and first performed in a broadcast the following year by the BBC Northern (now Philharmonic) Orchestra. A commercial recording by the London Symphony Orchestra under her compatriot, Mansel Thomas, followed, and it remains to this day her most popular work. The eight tunes she employs, virtually unknown outside Wales itself, are treated in the way her teacher, Vaughan Williams, used folk material in works like the Norfolk Rhapsody No.1. Here and there, she uses sequences and allusions to the Vltava of Smetana and The Bartered Bride, which some might consider incongruous, but they must have been cousciously made, even if their significance eludes the listener at this distance in time.