The changes are being introduced ahead of the outcome of a court case over fees charged by banks for unauthorised overdrafts.

Banks currently make up to £3.5billion a year from these charges, with fees as high as £35 for a single bounced cheque.

But they could lose some or all of that income and be hit with a £10billion bill for refunds if the courts decide those charges must be scrapped or capped.

Cristina Rebollo, of the price comparison website uSwitch.com, warned: “The UK is one of the only places in the world that doesn’t charge for current accounts.

“Customers have enjoyed free banking for 23 years but the current backlash against charges for items such as overdrafts and bounced cheques could serve as catalyst for the fast introduction of flat monthly fees on current accounts.”

Around 8.5million people in the UK pay for “packaged” accounts which come bundled with extras such as travel or phone insurance and breakdown cover. Fees range from £6 to £25 a month. But these paid-for accounts still make up a small proportion of the 120million current and savings accounts.

Moneyfacts.co.uk spokesman Andrew Hagger said banks would not start charging for current accounts until after the court case ends.

“I don’t really see anyone coming out with a fee-charging current account in the interim,” he said. “No doubt they will be thinking about it behind the scenes.”

Lloyds TSB has increased its monthly gold and platinum account fees by £2 each to £12 and £17 respectively from May 1. NatWest, which is part of the Royal Bank of Scotland group, will raise monthly charges from May 31 for its Advantage Blue and Gold accounts by 95p to £6.95 and £12.95.

The banks deny the increases are linked to the impending decision on overdraft fees, saying they reflect the increased services bundled with each deal. Lloyds TSB said it was the first increase in four years. But experts said banks were looking for alternative sources of income and warned there would be more increases in charges to come.

Doug Taylor, of consumer group Which?, urged customers to think twice before paying for a packaged account. “For most people they are not a particularly good deal.”