Millions of Lloyds, Halifax and Bank of Scotland customers will be charged overdraft interest rates of up to 49.9% from April and those with a poor credit history are likely to pay the most.

Lloyds Banking Group – which owns all three brands and has 22 million current account customers – is the biggest bank so far to overhaul its overdraft costs in response to a ban on excessive fees demanded last year by the City regulator.

It is the highest overdraft interest rate announced to date, and the consumer expert Martin Lewis’s MoneySavingExpert website called it “eye-watering”. .

The new industry rules have been brought in by the Financial Conduct Authority after it said the overdraft market was “dysfunctional”. The rules stop higher prices being charged for unauthorised overdrafts than for authorised ones, banning fixed daily or monthly fees for borrowing in this way. Instead banks have to price overdrafts using a simple annual interest rate.

But some commentators have warned that banks and building societies would attempt to make up their losses by imposing higher headline overdraft rates.

Nationwide became the first major provider to respond by introducing a single 39.9% rate, and several others have announced the same rate, including HSBC and Santander.

The Lloyds group said the majority of its customers would charged 39.9%, but some would receive a higher rate of 49.9%. The bank refused to say how many people that may be, saying: “As a result of these changes, 90% of customers with an overdraft will pay less than they do today.”

The group charges 1p a day on every £6 borrowed up to £1,250, 1p a day for every £7 borrowed between £1,250 and £2,500, and 1p a day on every £8 borrowed above that.

Lloyds said it was adopting risk-based pricing on its overdrafts, where the rate an individual is offered will depend on their credit history and other details.