TSB says it plans to grow its balance sheet by 40%-50% over the next five years.
The bank is aiming to become a larger player in the current account market, growing from 4.2% to 6% during that time.
Chief executive Paul Pester says it has already seen four to five as many people opening accounts every week since the TSB brand was re-launched last September than it had before.
Growth plans will also see TSB mortgages becoming available through brokers again from the start of next year.
More top news
Ricardo Medina is charged with stabbing his flatmate to death with a sword.
Police are hunting a man who is suspected of grabbing an 11-year-old girl who only got away by biting her attacker's hand.
The storm is expected to hit the country's southern coast on Monday.