Apparently ‘Liverpool Undenominational College’ was very nearly the name of the institution before the founders decided on Edge Hill. The original rationale was to provide teacher training without preference according to religious persuasion, hence un- or non-denominational. It is sometimes said that Edge Hill was founded on secular humanist principals, but it seems to me that this was not the case. In the early days the religious affiliation of students was documented, although records seem to have only allowed fror ‘Church of England’ or ‘non Conformist’ as the choices. The day started with prayers at 7am with more at 9pm (before silence at 9.45 and lights out at 10.) On Sundays, students were supposed to attend the church of their denomination and had to give a verbal reason if they had been less than twice. (Edge Hill University College: A History by Fiona Montgomery remains the authoriattive work on this period.) So it was non-denomination rather than non-religious.
Somewhere along the line these rules have been relaxed and I doubt if many students follow such a strict regime any more. However I do think the founding principle is reflected in today’s ‘widening participation’ policies and practices.