It was invented by a British person in Scotland and is beloved throughout the UK. Why wouldn't it be the national dish of Britain? The man who invented it, Ali Ahmed Aslam, was born in Pakistan, but had lived in Scotland since he was a small child, meaning he grew up steeped in British culture.

I don't think a cuisine has to be based on cooking that originates in a different country to be a country's national dish. He decided to improvise a sauce that was not especially South Asian considering it contained a New World fruit in his restaurant in Glasgow and that inspiration became the favorite food of millions in Britain.

Makes complete sense to me.