I’ve often wondered why Brits say “to hospital.” But we say, “She went to school,” not “she went to THE school.”
It reflects a difference in the way we think about these things. Going to school implies that a certain process is happening; it is more than a place, it is an institution. The same goes for "going to jail." If you want to specify that you are going for a purpose other than learning or incarceration, you would specify that you are going to the school, or the jail. The hospital, however, does not have a specific process associated with it. You could be going for any number of reasons: for treatment, for observation, for testing, etc. Since there is no specific process associated with the hospital, we go to *the* hospital. Brits, apparently, consider that the hospital denotes a process.