Actually, lots of schools in parts of the UK are very keen on promoting a "national identity" - just not a "UK identity".
When you have parts of the UK whose own (unofficial) national anthem is about a 700 year old war against other parts of the UK then it no wonder that a single "national identity" has never really caught on.
When you have parts of the UK whose own (unofficial) national anthem is about a 700 year old war against other parts of the UK then it no wonder that a single "national identity" has never really caught on.