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
Sir Bruce Forsyth had to be rushed to hospital after a fall at his home.
Figures show seal shooting is on the decline but 51 licences were granted this year permitting the cull of more than 850 marine mammals.
Three goals were enough to send the team through to its first major football tournament finals since the World Cup in 1986.