Williams was the eldest son of Peter Williams, rector of Llansannan, Denbighshire, and his wife Lydia Sophia Price, daughter of the Rev. James Price of Plas-yn-Lysfaen, Denbighshire.
The school is the predominant Welsh language school in the area, and it serves pupils from a wide area including Abergele, Colwyn Bay, Betws yn Rhos, Conwy, Llandudno, Llanfairfechan, Llansannan, Penmaenmawr and Eglwysbach.