TSB's profits for the three months to 31 March 2015 increased by 153.3% to £34.2 million compared to Q4 2014.
Speaking to the BBC, Mr Pester said:
"We believe we're Britain's biggest challenger bank but we really want to take on the big guys. If that means rolling up some of the smaller banks we would consider doing that."
The bank also received over £700 million of gross mortgage applications through the newly launched TSB mortgage broker service to the end of the first quarter.
Since launching its mortgage intermediary distribution channel in January 2015, TSB has received over £700 million of applications and approximately £100 million of completions in the first quarter. It has now expanded to offer re-mortgage products and has begun a pilot for buy-to-let mortgages.
In TSB's Q1 statement, Paul Pester said:
“TSB is starting to fire on all cylinders as we take on the big banks in our mission to bring more competition to UK banking.
"Over 7.9% of people opening or switching a bank account in the last quarter chose TSB – meaning we’ve now had five quarters in a row where we’ve beaten our 6% target; our mortgage broker service has continued its flying start, having received over £700 million of applications by the end of March, and more customers than ever before are recommending TSB to friends and family.
"Whilst we still have a long way to go in bringing better banking to UK consumers, we’re making real progress. This is reinforced by Banco de Sabadell’s recommended offer to acquire TSB, which is a real vote of confidence in everything we’ve achieved so far and in our potential to succeed further in the future.”
Last month, Spanish bank Sabadell and TSB Banking Group reached agreement on a £1.7bn takeover.
