My first thought would be “cocker spaniel”.
Must be due to AMA pressure.
That’s a good question. The rules of how articles are used in a language are quite characteristic, and for non-native speakers they can be difficult to learn even in English with no genders or case inflections to worry about. It’s not surprising that different dialects of English sometimes vary in that respect; similar situations exist in other languages. For instance, words exist in German that have different genders depending on the region or country, and I’m told even the sociolect though I don’t know any specific examples of that.
I’ve always wondered why American English kept “gotten” and “fall” (autumn) but we lost “fortnight”, which would obviously be a very useful word to have.
It’s never occurred to me that Americans don’t use it. Things you learn!
Also on the question of articles, in my time high school students went to the prom, but today’s high school kids go to prom. I think it was sometime in the last 25 years that the article disappeared. And. it’s hard to ask about it online because you get a lot of young people who are trying to help but totally misunderstand the question.
So maybe we’ll be saying “in hospital” too, before long.
Do the British say “I am going to bank” or “I am going to supermarket?”
No. Somehow, “hospital”, “school”, “court” and “university” have a special article-free status.
I think the difference is that in Alessan’s examples the speaker has a definite destination in mind. It matters which bank you go to, and even the supermarket will normally be one’s local, regular supermarket. Whereas talking about logistics for a holiday, I suspect I would say “On the first morning, we’ll have to go to a supermarket” because I don’t have a specific one in mind.
Whereas with your examples, English takes a more abstract view. What matters is the function of the institution, not its location or even anything specific about it. I think this is in part because you get little choice in the matter - which hospital or court you go depends more on the nature of your predicament, for example. (This doesn’t work for university). But perhaps more because these are institutions where what matters is the process - you enter and emerge cured (or not), educated, or in receipt of justice. Things are to a certain extent being done to you, whereas in supermarkets and banks you are transacting.
Also interesting is that the article reappears when we specify the instution - He’s in the children’s hospital, I’m going to the High Court, we’re sending our kids to the Catholic school etc.
What Stanislas said!
Although just to add somewhat cheekily to respond to Alessan… I’m sure some Yorkshire folk may say “I’m just nippin’ t’ supermarket” or “I’ve got to pop t’ bank”.
Interesting analysis, @Stanislaus.
One interesting is that it applies to all types of educational institutions - school, college, university, kindergarten, etc. - but it doesn’t apply to all types of medical institutions. You wouldn’t say “I’m going to clinic”, would you?
Also, “work”.
This is because “work” is an abstract state of being where there may or may not actually be any of it happening.
No I would say “the clinic”? I think because again - even though what kind of clinic isn’t specified - it is a specific service whereas hospital is general. That said, I would also say “I took my daughter to A&E” so…in conclusion, English is a land of contrasts?
Just to check though, what do you mean by clinic? If it’s primary medical care, then this is also different because I would say “I’m going to the doctor”. Or I would also say “I’m going to the dentist”, making the role stand in for the institution.
Now that you mention it, maybe that’s related to the reason for the article-free hospital , school, court, church. I’m in the US and if I say someone is “at school” or “in college” it doesn’t mean they are physically there at this moment and if I say “at church” or “in church” it means they are physically there at this moment but not to participate in anything related to a religious service. They might be at the church fixing the wiring or painting the wall.
But if you say “I’m at work”, that means that you’re physically at your office or whatever.
That’s why I said “related” 
- but really, “at work” doesn’t necessarily mean exactly the same thing as “physically at my office or other regular work location” , It might for some jobs, but not all. There have been many times I was at my office but not “at work” and even more times that I was “at work” but not at my office.
To complicate it further, you can also be “at work” on something that isn’t even your actual vocation. I can be at work on my garden, or at work on my car, or even at work on my stamp collection.
I think the conclusion is that English is a land of very few consistent rules. It’s what makes it so beautiful for lyricists and maddening for language teachers.
Whereas an American would say “I took my daughter to the emergency room.”
On the other hand, if that same American decided to go to an urgent care clinic instead, they might say “I took my daughter to urgent care.”
I genuinely thought “A & E” was a British grocery chain or something.