TSB is set to replace all its 0845 numbers with local-rate 0345s for customer services numbers in the coming months.
The 0345 numbers will also be rolled out for all retail and business banking and TSB will use 631 local numbers for all of its branches.
Free 0800 numbers will continue to be used for fraud and complaint helplines.
The bank said 0345 numbers will always be included in inclusive minutes for both landlines and mobiles, and TSB will not receive any income from these calls.
Peter Navin, managing director for branch and business banking at TSB, said: "We want to be transparent with our customers and believe the introduction of 0345 numbers will make it more convenient for customers to get in touch without worrying about any surprise costs."
In August 2013, the government announced it is to outlaw the use of 084, 087 and other "rip-off" telephone numbers for enquiries and complaints.
According to research by Which?, nearly two-thirds of Brits think companies use high-rate numbers to discourage them from calling and four in five people think companies who make them call high-rate numbers don’t value them as a customer.
The 0871 numbers Which? analysed typically cost at least 10p a minute to call from a landline but could be "substantially more" from a mobile phone.
It also found that 0844 and 0871 numbers are not included as standard in inclusive call packages from landlines or mobiles.
Richard Lloyd, Which? executive director, said: "Well done to TSB for dropping high-rate numbers and responding to the needs of its customers who now won't have to pay a premium to ask a question about their account.
"We have been campaigning for all companies to end costly calls, and TSB is showing there's no reason why other banks can't follow suit."