Priscilla Wakefield established the Tottenham Female Benefit Club and Children’s Bank in Tottenham in 1798. Anyone could open an account for a child by making regular monthly contributions of a penny or more with annual interest accruing on the deposits. The Benefit Club was recognised at the time “as the first distinct Bank for Savings publicly set on foot for the benefit of the lower classes”.

On 1st January 1804 Priscilla Wakefield inaugurated her Tottenham Benefit Bank into which deposits of any amount could be made and interest of 5 % was paid on deposits of a pound or more.  The design of the bank was based on the Benefit Club and that 'the bank was opened by an orphan girl of fourteen, who placed L.2 l£2] in it, which she had earned in very small sums, and saved in the Benefit Club.'  
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The life and economics of David Ricardo

Priscilla Wakefield: forgotten pioneer of financial services for the poor
Diary Entries from 1798 on the First Savings Bank from the Open Book Blog
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The life and economics of David Ricardo by John P. Henderson et al, Kluwer Academic Publishers, 1997
The Palgrave Handbook of European
Banking, 2017
Encyclopaedia Britannica 1824
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Encyclopaedia Britannica entry See also the Report of the Society for Bettering the Condition of the Poor on the Account of Savings Bank page
 Reports of the Society for Bettering the Condition of the Poor
​referred to in the Encyclopaedia Britannica entry above 
The Athenaeum, 1847: article and correspondence on the The Founder of Savings Banks
Issue No 1012: Article by 'E.F' on 15 March stating that 'the first Savings Bank was established in Tottenham (October 22, 1798) by Priscilla Wakefield - a name unknown to our biographical dictionaries'
Issue No: 1016: Letter from 'JC', Honiton on 7 April argues that the Reverend Henry Duncan in Ruthwell, Scotland, first proposed the scheme for Savings Banks for general adoption in 1810.
Issue No 1018: Response by 'EF' later in April discusses the role of Rev Duncan but that 'it was equally certain that Priscilla Wakefield was 'the founder of savings banks' - both as having suggested the system now adopted and as the first to put it in practice'.
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Post Office Savings Bank today
The Post Office Savings Bank and National Savings, which remains state-owned in the UK, is now known as The National Savings and Investments (NS&I). NS&I is one of the largest savings organisations in the UK with 25 million customers and £147 billion invested. NS&I is both a government department and an Executive Agency of the Chancellor of the Exchequer.

NS&I traces its origins back to 1861 - sadly there is no acknowledgement of the efforts of Priscilla Wakefield of Tottenham sixty years before that date which prepared the ground for the Post Office Savings Bank.