TSB Banking Group has hailed "a strong start" to its independent life with an 8.4per cent share of all people switching or opening a new bank account in 2014.

The bank, floated last June when Lloyds Banking Group sold a 38.5 per cent stake, said 500,000 new bank accounts were opened with it last year, helping to drive its pre-tax profit up 2.3per cent to £133.7million.

TSB has 185 of its 631 branches in Scotland, legacy of the original Trustee Savings Bank business absorbed by Lloyds in 1995.

The bank's shares jumped 30p on the first day of trading to 290p, with the new shares 10 times oversubscribed, but yesterday they closed just below the offer price at 259.6p.

Lloyds sold off a further 11.5per cent tranche last September.

Currently the UK's seventh biggest lender, TSB has none of the conduct overhang affecting the established players, a clean balance sheet, and is aiming to become a larger player in the current account market, growing its market share from 4.3per cent to 6per cent over the next four to five years.

Paul Pester, chief executive, said: "Growth remains our key strategic focus and we expect TSB to continue to consistently attract more than 6per cent of all new and switching bank accounts each quarter," said chief executive Paul Pester.

Last week close rival Nationwide said it had won 8.6 per cent of current account switchers last year, lifting its overall market share from 6.2 to 6.7 per cent.

Asked about speculation that TSB might snap up smaller challenger Aldermore, which is planning a stock market listing next month,

Mr Pester hinted that he might be interested. "If we have the right assets at the right price and they make sense to our shares, then we would look at them," he said.

The bank said it had received over £300m of applications to date for its mortgage range which it opened to brokers for the first time in January.

Analysts at Citi said: "This seems to suggest that the risk is to the upside on management's £1.5bn loan growth target for 2015."

Lloyds was forced by European regulators to sell the 631 branches which now form TSB as a condition of receiving state aid during the financial crisis.

Originally Lloyds planned to sell the branches to the Cooperative Bank. When the deal fell through, it decided to resurrect the TSB brand as a standalone business and sell it to investors.

UK regulators are keen for new banks to challenge the 'big four' lenders, who still provide three-quarters of the country's personal current accounts.

Lloyds has to sell its remaining 50 per cent stake by the end of 2015 and was free to start selling more shares in the company from yesterday.