Bank of England
Bank of Scotland
Bank of Ireland
Royal Bank of Scotland
Clydesdale Bank

http://en.wikipedia.org/wiki/British_banknotes
Pound sterling banknotes are issued by
the Bank of England accepted throughout the UK;
the Bank of Scotland (generally accepted throughout the UK);
the Royal Bank of Scotland (generally accepted throughout the UK);
the Clydesdale Bank (generally accepted throughout the UK);
the Bank of Ireland, First Trust Bank, Northern Bank and Ulster Bank (rarely seen outside Northern Ireland).
Sterling banknotes are also issued by the Government of the Isle of Man and the States of Jersey and the States of Guernsey, but their notes are not generally accepted off their own islands (although Guernsey notes can sometimes be found in Jersey and vice versa).