It's a really alien concept to me. We don't have much anything like it.
In my Junior School, which was a Church of England school, we would have a weekly religious assembly (which you didn't have to go to and most non-christians didn't), and a local vicar would visit, give bible stories/lessons and we'd sing some christian songs. The only thing we always did was the Lord's Prayer. But no one was going to force you to say it.
And this was unique to CofE schools.
In regards to the National Anthem, that is pretty much never taught in schools, or at least wasn't in mine.
I'm kind of ashamed that I don't really know it.