As you know, the Bank of England orders banknotes to be produced. However, these are only legal tender in England and Wales - that is, the area covered by English law. They are not legal tender in Scotland or Northern Ireland - however, they do still circulate there and are used there. Furthermore, Scotland or Northern Ireland each have their own national circulating banknotes, which are issued by their respective banks.
According to Wikipedia:
Currently, three retail banks are allowed to print notes for circulation in Scotland; Bank of Scotland, Royal Bank of Scotland, and Clydesdale Bank. Such banknotes have to be backed one to one with Bank of England notes.
Northern Ireland has four issuers of banknotes:
Bank of Ireland notes
First Trust Bank notes
Danske Bank/Northern Bank notes
Ulster Bank notes
Technically, none of these issues is legal tender. That puts them in the same position as tokens: money that is not issued by the State. What is the name for banknotes that are not legal tender but are still money? Are they just paper tokens?