In a majority of parishes there is a vicar, and crucially the historic university college or other rectory-owning major landowner only sold their land free from tithe under the Tithe Acts so they, or more commonly, the local church, bear the liability for the local chancel.
In most parishes, there is a priest, and importantly, the large landowner who owns the university college or rectory only sold their land without having to pay tithe under the Tithe Acts, so it's usually the local church that takes on the responsibility for the local chancel.