About 8 million HSBC customers are to have their overdraft rate doubled – and in some cases quadrupled – to 39.9% as it becomes the biggest UK bank so far to respond to tough new borrowing rules.

Some customers – potentially running into the millions – will now pay more for going into the red as a result of the move, which comes after the Financial Conduct Authority ordered a ban on excessive overdraft fees.

HSBC’s new single rate for all overdrafts matches the 39.9% rate announced by Nationwide in July. However, there was disagreement about how many HSBC customers will pay more than they currently do.

The MoneySavingExpert.com said it was highly probable that the majority of customers who had gone into their authorised overdraft would be worse off, but HSBC said that seven in 10 people who used their overdraft would either be charged the same or less because some charges had been removed or reduced.

However, HSBC’s argument still points to potentially millions of customers – or three in 10 account holders who use their overdraft – paying more if they are overdrawn.

HSBC, which has between 8 million and 9 million current account holders and a 14% share of the UK market, said the new higher interest rate would apply to authorised and unauthorised borrowing across its whole range of accounts except for its student bank account.

The new rate is double the 19.9% that the bank now charges holders of several of its main accounts for an authorised overdraft. However, for some customers the increase is a lot more than that: HSBC’s Jade bank account has a 9.9% rate at the moment, while customers of its Premier account are currently charged 11.9%.

HSBC is the biggest name so far to respond to the FCA’s clampdown announced in June, which the regulator said would make overdrafts simpler, fairer, and easier to manage.

The new 39.9% rates follow warnings that while the shake-up would benefit more vulnerable consumers, it could lead to firms seeking to make up the losses they would suffer by imposing higher authorised overdraft rates. Other banks are expected to announce higher headline rates over the coming weeks.

The FCA announced in June it would be stopping banks from charging higher prices for unauthorised overdrafts than for authorised ones, banning fixed daily or monthly charges for borrowing in this way, and requiring banks to price overdrafts using a simple annual interest rate.

The watchdog had called the overdraft market “dysfunctional” and said it was causing significant consumer harm.

There are 26 million UK overdraft users, and they are a huge cash cow for banks, which made more than £2.4bn from them in one year alone (2017).

While the new rules do not take effect until April 2020 at the latest, banks have to give their customers notice of changes. In addition to the new rate, HSBC’s shake-up – which comes into effect on 14 March – includes the removal of a £5 daily fee for going overdrawn without permission, a reduction in the maximum monthly charge from £80 to £20, and the introduction of an interest-free £25 buffer on many accounts in order to provide some leeway should a customer accidentally nudge into the red.

The ban would lead to a big reduction in costs for some people who may be struggling financially. A customer overdrawn by £200 for 15 days without permission would have the amount they are charged slashed from £80 now to £2.78 under the new structure.

Andrew Hagger, the founder of the financial website MoneyComms.co.uk, said: “Paying almost 40% for agreed overdrafts looks like becoming the norm, even if you have a top-notch credit record – double the rate on credit cards. Surely this isn’t the outcome the regulator was expecting?”

In June the FCA had indicated its clampdown “could create winners and losers, as firms would be likely to seek to recover lost overdraft revenue from within their overdraft offering by, for example, increasing arranged overdraft prices”.

It said the net effect would be better for the public overall because these changes would “reduce the burden … on vulnerable consumers, whose welfare we are particularly concerned about”.