By Daniel Hunter
TSB was responsible for 8.4% of all people switching or opening new bank accounts in 2014, leading the bank to describe it as a "pivotal year".
The bank, which was split from Lloyds Banking Group in June, said half a million new bank accounts were opened last year.
The increase in bank accounts resulted in profits of £133.7m, an increase of 2.3%.
The bank is currently the seventh biggest lender in the UK and is planning to increase its market share from 4.3% to 6% over the next five years.
"Growth remains our key strategic focus and we expect TSB to continue to consistently attract more than 6% of all new and switching bank accounts each quarter," said chief executive Paul Pester.