Soundcore Q20 are somewhat less than £200. They sound OK. My children preferred them to the Beats Studio Pro 3s they had previously. They survive well with adolescent use. And are not heart-breaking when they inevitably get stood on, bent, or lost.
An alternative to which one of our children has swapped are JBL Live 660NC. More stylish than Q20s. Noise cancelling, nice sound, fairly robust. And less than £200 by a margin.
edit ++ to what @cynic-al wrote. While it’s nice to give children fancy things on the whole as long as it works, looks cool, and parents will not go off the deep end when it breaks it’ll be fine.
have you considered just giving them £200 and asking them to buy what they want?