That's certainly true and they are illegally working. But maybe your image of a student might be a bit narrow? There's a large industry in Europe of language schools. You pay the school/country a few thousand euros/pounds and in return you get a student visa + basic language course. Not all, but many students are coming from pretty bad places in the hope of somehow landing a work visa(Italy and Portugal will grant citizenship if you can prove ancestry for example). The friends of my wife that told me about their lives/this practice, none of them where working for "spending money".