> cathedral cities like Cambridge or Oxford

Oxford cathedral is actually the college chapel of Christ Church, a college of Oxford University. It's not open to the public. You need a letter from your anglican parish priest confirming that you are a church member if you want to visit.

It's not even a landmark; the chapel is inside the college walls, and barely visible from the street. The striking tower over Christ Church (Tom Tower) is over the college gatehouse, and not part of the chapel.

Tom Tower, by the way, is named for Great Tom, the bell that chimes the hours. It used to chime local time, which in Oxford is nine minutes behind UTC. Nowadays it chimes UTC hours (formerly GMT).