He believes the innovation in finance could eliminate the need for maturity transformation – the process by which short-term deposits, such as current accounts and instant access savings, fund long-term loans including mortgages.
That is a fundamental principle of the industry as banks can offer a low interest rate to savers while charging more to borrowers, profiting from the gap between the two rates.
Yet in 10 to 20 years’ time, he believes the need for banks to perform the function might no longer exist – already some investors are sidestepping banks by using websites to match borrowers and savers directly.
In a speech at the Institute of Chartered Accountants in England and Wales the former chief executive said banks will have to face up to extraordinary changes in the coming decades.
While they are not going to undermine banks – instead Mr Jenkins believes the switch away from high street banking and onto mobile phones is led by customer demand – the changes do present challenges.
He expects banks will close around half of their branches in the coming decade, and predicts that between 20pc and 50pc of all bank jobs will be chopped as customers are served via technology.
While keeping up with the latest technology, banks will still be hampered by aging computer systems, he fears.
Mr Jenkins’ time in charge of Barclays, from 2012 to 2015, was dominated by his efforts to reform the bank’s culture in the wake of the Libor manipulation scandal.
Despite his efforts he was turfed out of the job last year by new chairman John McFarlane who wanted a boss who would focus more on streamlining the bank and boosting its profitability.
Mr Jenkins is continuing to stress the importance of the cultural shift in banking if lenders want to end the stream of regulatory investigations and fines, and win back the trust of their customers.
Chief executives are crucial to such initiatives, he said in a recent private speech: “Leadership is the most important thing about culture.”
First appeared at the Telegraph