Shares in TSB edged ahead as the bank revealed a profits lift and hailed an above-target performance in the current account market.
The revived brand, which floated on the stock exchange earlier this year, posted a 28.8% increase in third-quarter pre-tax profits to £33.1 million.
However, it said its growth prospects were being held back by the low level of switching among UK bank customers and a decline in home loans.
TSB said it had signed up one-in-10 of all customers opening new current accounts or switching in the UK, but admitted that pace of growth was likely to fall back to its long-term target of 6% as the steam runs out of its launch campaign.
Customer deposits grew by £500 million to £24.2 billion over the three months, but loans and advances shrank by £477m.
Chief executive Paul Pester said: “We are probably now at base camp where it comes to growing our share of the current account market. But we are probably in the foothills where it comes to mortgages.”
The CEO also admitted 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 last year under European rules on state aid after it received a taxpayer bail-out during the financial crisis.
TSB returned to the stock market in June for the first time since its 1995 merger with Lloyds, in a float that raised £455 million.
A further share sale last month raised £161 million and saw Lloyds’ stake cut to 50%.
It must dispose of its holdings in the business by the end of next year.
Mr Pester said customers were showing faith in the brand.
He said: “While we have always been clear that we are on a five-year journey to grow TSB and its returns, it’s great to see people right across Britain continuing to vote with their feet for TSB’s local banking model.”
TSB shares closed 4.3p higher at 263.3p.