Paul Pester told The Yorkshire Post that TSB was offering “high street banking, not Wall Street banking”, after new figures showed it was picking up nearly one in ten of all new current accounts being opened in the UK.
Mr Pester said the bank was receiving a consistent message from its customers: “They wanted a transparent bank that was there to serve them and their local community. We have got a website called ‘truth and banking’.”
He said TSB could trace its roots back to the savings bank movement of the early 19th century.
He added: “We’re a brand new bank, that’s 200 years old.”
TSB returned to the stock market in June for the first time since its 1995 merger with Lloyds, in a float that raised £455m. A further share sale last month raised £161m and saw Lloyds’s stake cut to 50 per cent. It must dispose of its holdings in the business by the end of next year. TSB said it was ahead of a target to grow its share of Britons’ personal current accounts to six per cent in the next five years.
It currently has a 4.2 per cent share of the personal current account market.
Pre-tax profits for the third quarter of 2014 rose 28.8 per cent to £33.1m.
Customer deposits grew by £500m to £24.2bn over the three months but loans and advances shrank by £477m.
Mr Pester also said TSB would continue to lose mortgage customers through to the start of 2015 before starting to grow later in the year.
“Our mortgage book is shrinking. Quite a big chunk was written through mortgage brokers several years ago,” Mr Pester said.
“As our customers change their mortgage we are not able to remortgage them through TSB.”
Many borrowers would have taken out their loans when the bank was still part of Lloyds - which spun off the business under European rules on state aid after it received a taxpayer bail-out during the financial crisis.
Andrew Tyrie, chairman of the Treasury Select Committee, said this week that there was a danger that TSB might struggle to grow significantly and act as a challenger in the market.
Mr Pester said TSB was well-placed to compete with the bigger banks.
He added: “We have everything we need in order to enable us to be a real competitor in the UK market and to reinforce our position as Britain’s challenger bank.
“The fact that one in 10 customers chose to switch to us is a very good sign of that,” he said.
TSB has 38 branches in Yorkshire, and employs around 300 staff in the county. TSB, which listed in June, said that its 9.7 per cent share of new current account openings during the third quarter of 2014 put it on track to grow further.
“We feel that rate of current account openings may well fall back but the six per cent target appears eminently feasible, in our view,” said Mirabaud Securities analyst Alex Potter.
British regulators are keen for new banks to challenge Britain’s big four lenders - Lloyds, Royal Bank of Scotland, Barclays and HSBC, which provide three-quarters of personal current accounts.