A few notes on terminology: Great Britain is a geographic term, not a legal one. Great Britain is an island divided between England, Scotland and Wales which all, along with Northern Ireland, form the United Kingdom. The demonym of United Kingdom, confusingly, is "British". Sometimes "Great Britain" is used to specifically refer to the UK without Northern Ireland, though there are plenty of parts of England, Wales and especially Scotland that are also not on Great Britain.

Anyway, to answer your question: the currency of the entire UK is Pound Sterling, which is the same everywhere: £1 in London is the same as £1 in Edinburgh. Some Banks in Scotland and Northern Ireland have permission from their respective devolved governments to print their own banknotes, but they must be backed by Bank of England notes stored in a vault and, importantly, they are not automatically accepted elsewhere. Some large retailers will accept them, but shops in Northern Ireland, England and Wales are under no legal obligation to accept a Scottish banknote, whereas the Bank of England notes are accepted everywhere.

Also, while the banks that issue notes in Northern Ireland and Scotland are just regular, privately-owned commercial banks, the Bank of England is entirely publicly owned and doesn't offer much in the way of traditional commercial banking services.