Why do British people not put “the” in front of hospital?

“It’s called the zero article, and is used for institutions. The sentence describes a state of being rather than the physical location. A patient is both in the hospital and in hospital, but their doctor is only in the hospital.

This is the same as how a teacher and a student are both in the school (located in the school building), but only the student is in school (being schooled)."