TSB hailed an above-target performance in the current account market today but said it was being held back by the low level of switching among UK bank customers.
The revived brand, which was floated earlier this year, is also suffering a decline in home loans as they will not be available through mortgage brokers until January.
Pre-tax profits for the third quarter of 2014 rose 28.8% to £33.1 million. Shares rose 3% on the results.
TSB said it had signed up one in ten of all customers opening new current accounts or switching in the UK but admitted that following a launch campaign the pace was likely to fall back to its long-term target of 6%.
Customer deposits grew by £500 million to £24.2 billion over the three months but loans and advances shrank by £477 million.
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."
Mr Pester admitted the sluggish level of current account switching in the UK was putting the brakes on plans to grow market share from around 4.2% to 6% in the next four to five years, despite success in capturing the new business that was available.
He 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 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's stake cut to 50%. It must dispose of its holdings in the business by the end of next year.
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