First Direct will become the first leading bank to charge its customers for a standard current account.
The bank will charge customers £10 a month to hold a current account unless they deposit or maintain a balance of at least £1,500 a month.
But chief executive Chris Pilling said: "I would contest whether it is the end of free banking as we know it."
Defending the move on BBC Radio 5 Live, he said the bank enjoyed the "upper end of the demographic profile" in its customers.
About 200,000 customers are thought to be affected by the move, but it is feared other high street banks may follow suit.
Mr Pilling said that First Direct, whose parent company is HSBC, was a "small, but perfectly formed bank so we have a good reputation for customer service".
Addressing customers, he said: "If you do .125want to stay.375, either please put more money into a relationship with First Direct, or buy a product from us, or pay the fee."
Explaining what such a product would be, he said: "Either ... take a loan from us, a mortgage from us, or an insurance product."
But he said it was "a small minority of customers" - up to 200,000 - who would face the charge.
"There are two types of customer who will be affected by it," he said.
The first he described as the bank's 40,000 "dormant customers ... eventually that's a cost to us".
There are also those who use their First Direct account as a "secondary account", he said, for between five to 10 transactions a year.
The "vast majority" of customers - 85 per cent - would not be affected by the charge, he said, but the current situation was "preventing us from servicing these customers properly".
He said of the move: "Inevitably there will be some silliness about conversations and rhetoric and the debate that will ensue on that."
Consumer organisations such as Which? and The Consumer Action Group have already expressed concern about the charge.
But Mr Pilling denied that the industry had decided en masse to introduce charges on current accounts.
"Good grief no," he said. "That would be unheard of. I don't believe that would even be allowed."
He said of First Direct: "This brand does things other companies do not do."
Most banks already charge fees for premium accounts, but soften the blow with extra services such as breakdown cover or travel insurance.
First Direct was the first bank to offer 24-hour telephone banking in Britain when it launched in 1989.