I live in England and am 16 yrs old, and I can tell you that at Christmas at my first primary school, they played last Christmas on repeat for several hours so now I despite that song and all things Wham! lol. I don't really know the lyrics to any other Christmas songs. I used to play the Rudolph reindeer one on my saxophone but apart from that nothing. My second primary school was very religious and we sang more Christian type songs in the chapel we had on the school grounds. (Private school not all schools have chapels lol) In secondary school Christmas is less of a prominent aspect as it is significantly more mature than primary schools as it is from age 11-18 so the most Christmas celebration we have is watching a movie. There is also a lot of diversity in schools and some of the Jewish or Muslim etc would not be happy if our school was commandeered by a Christian holiday.
I am not saying that this is what school is like for all British people, because I have not spent Christmas at every school in the country, but this is what it was like at my schools.