In Britain alone millions of people make formal complaints each year about their banks. For them, Sebastian Siemiatkowski, founder of Klarna, a Swedish payments startup, brings good news. New European rules, he says, will open the door to a host of innovative services that analyse transactions, so “an app could tell you there’s a cheaper mortgage available and start the switching process for you.” Apps could warn account-holders if they spend more than a predetermined amount or are about to become overdrawn, or even nudge them to save more. Customers need barely ever interact with their bank.

To date, despite dire warnings, European retail banking has been remarkably unscathed by technology-driven disruption. Customers stay loyal, and banks still do the most of the lending. Financial-technology (“fintech”) companies are beginning to mount a challenge, most conspicuously in the online-payments industry in northern Europe: Sofort, iDEAL and other fintech firms conduct over half of online transactions in Germany and the Netherlands, for example. But their reach is more limited elsewhere in Europe. Physical payments are still overwhelmingly made with cash or bank cards.