The use of 'High School' is becoming more common in the UK, but I usually say Primary School and Secondary School.
Just Primary school and high school in general. In some places high school can be split into junior and senior and in England you get sixth form colleges too.
I am from Australia and we have primary school until grade 6, and then highschool from year 7 until the end. There is nothing called middle school. I imagine it's similar in the UK.
As far as I know elementary school is called as 'primary school' but I am not sure. .
I put "elementary school, middle school, and high school" and it marked it as wrong when it actually should be right. This is what i dislike about programs like this. They don't offer multiple variations of correct answers.
I'm not sure what was marked wrong. I prefer primary school and senior-high school (as I never understood why high school doesn't include junior-high school in N. America) though I may be mixing British and American terms with an old, disused hyphenation style.