Britain's newest bank, TSB, has rejected claims that it is too small to compete and says it is winning almost ten per cent of new bank accounts.

The Treasury Select Committee asserted this week that the collapse of the sale of the bank's 630 branches, 180 in Scotland, to the Co-operative and the flotation of a standalone TSB had left the challenger far less able to threaten the big four.

But chief executive Paul Pester said: "We have everything we need in order to enable us to be a competitor in the UK market and to reinforce our position as Britain's challenger bank. The fact that one in ten customers switch to us is a very good sign of that."

Mr Pester said the share was "well ahead of our long-term target" - a six per cent share within five years. TSB is the seventh-biggest high-street bank, with a 4.2 per cent share of the personal-current-account market

The bank said the strong current-account performance had helped it grow deposits by £500 million to £24.2 billion in the third quarter.

The TSB Classic Plus account, launched with a big media campaign on March 31, offers five per cent interest on balances up to £2,000, a higher rate - though lower limit - than its chief rivals Halifax and Santander. The latter two banks, along with Nationwide, are the only net gainers from the first year of the seven-day current-account switching service, according to Payments Council figures published last week - and Halifax is part of TSB's former owner Lloyds Banking Group.

TSB highlighted its Borrow Well marketing campaign, promoting the bank as a responsible lender, and its new mortgage campaign, which offers to pay customers' council-tax for a year up to £2,500. The bank said: "Initial customer reaction to both campaigns is positive."

But the absence of an intermediary channel for its mortgages saw net lending to its historic customers reduce by a further £300 million to £19.1 billion.

Mr Pester said the bank's plans to make TSB mortgages available through brokers from the first quarter of 2015 are on track. The bank aims to grow its balance sheet by up to 50 per cent over five years.

TSB said it had further improved a market-leading online and mobile banking service, and believed itself to be the first UK bank to appoint a chief digital officer, Ashley Machin, to its executive committee. At the same time it had "refreshed" 135 branches in 2014, with a target of more than 260 by the end of the year.

It said that in a recent Which? survey, TSB was ranked best high-street bank for customer service.

Statutory pre-tax profit of £33.1 million was up from £25.7 million in the second quarter though down on the £38.6 million in the third quarter of 2013

Alex Potter, analyst at Mirabaud Securities, said: "We feel that rate of current-account openings may well fall back but the six percent target appears eminently feasible."

The original Scottish-born TSB was swallowed by Lloyds in 1995.

When the Co-op deal fell through, Lloyds floated a 38.5 per cent stake in TSB on the London Stock Exchange in June, followed by a further 11.5 per cent last month.

TSB shares, floated at 290p, were up 3.1p at 262.1p.