If you are using just using 4 posts, I think that schools would better be suited as taxonomy terms rather than a post type. Associate your Posts with the school tax term. I would then create custom templates for each of those terms.
- taxonomy-schools-cambridge.php
- taxonomy-schools-teeside.php
- taxonomy-schools-newcastle.php
- taxonomy-schools-sunderland.php
Within those templates, use a WP_Query object to surface those posts. Read more about WP_Query taxonomy parameters here.
Your URLs would still be /schools/sunderland/ etc…
This seems like an easier out-of-the-box approach rather than creating new functions to do the same thing. Though, this comes down to UI preference at the end of the day.