Lloyds Banking Group and Royal Bank of Scotland have narrowly passed a Bank of England test to see how lenders would cope with severe economic stress.
The test, using the position of banks and building societies at the end of 2013, found both RBS and Lloyds would be susceptible to such a crisis.
However, improvements and changes to their plans this year meant only the Co-op was required to submit a new plan.
The Co-operative Bank has been ordered to shore up its balance sheet by axing £5.5 billion in loans after it failed a Bank of England stress test.
The Bank found that a severe downturn with house prices plunging 35% would wipe out the Co-op's capital because of the effect on its risky commercial property and sub-prime home loans.
The Bank of England is investigating whether its staff knew of - or even aided - the possible manipulation of auctions during the financial crisis, the Financial Times (£) reported.
The formal investigation was reportedly launched this summer. Sources told the FT the probe was assessing whether BoE money-market auctions in late 2007 and early 2008 were rigged to pump liquidity into the banking system.
A BoE spokesman told Reuters he could not comment on the details in the report.
"If the bank were conducting an investigation or review of any of its activities, as it does from time to time, it would be wholly inappropriate to provide a running commentary via the press," he added.
The Bank of England has said its chief foreign exchange (Forex) dealer was dismissed on Tuesday for serious misconduct relating to internal policies.
The central bank stressed that it was not related to the Forex rigging case.
Britain is "more than halfway" along the road to recovery, according to the governor of the Bank of England.
Speaking to the Sunday Times (£), Mark Carney said the economy had moved decisively from recovery to a full-blown expansion.
Mr Carney said: "Wherever the finish line was in the depths of the crisis, we are much more than halfway towards that finish line now", but warned that challenges still lie ahead.
The Bank of England expects the economy to grow by 3.5% this year, easily the fastest pace predicted for any advanced country. Unemployment is also expected to fall below 6% by the end of 2014, with 800,000 jobs created over the past year.
Interest rates have been at 0.5% despite speculation that some rate-setters on the Bank's nine-member monetary policy committee (MPC) might have voted for a hike. But an overall vote in favour would have surprised markets, with analysts focusing instead on the prospect of a rise towards the end of this year or early in the next.
In the second three months of the year gross domestic product (GDP) figures last month showed the UK had finally emerged from its worst downturn since the Second World War as output surpassed its pre-recession peak in early 2008.
Since then, survey data indicating strong growth in the dominant services sector has added to pressure for a rate rise - though a weaker performance for Britain's beleaguered manufacturers has led to calls for caution.
The Bank of England left interest rates on hold at 0.5% today.
The Bank left the scale of its quantitative easing (QE) programme to boost the money supply unchanged at £375 billion.
UK borrowers should expect interest rates to return to their pre-recession levels of around 5 percent within a decade, according to the outgoing Bank of England deputy governor for monetary policy.
Sir Charlie Bean who leaves his job tomorrow, said market expectations that the first increase in interest rates would come at the turn of the year were "reasonable".
He told Sky News: "The market has rates going up to 2.5% over next three years. That seems like a broadly sensible judgment."
Sir Charlie admitted that in the run-up to the crash, economists were "not sufficiently cognisant of the risks building up in the financial system" but insisted the economy is far more resilient than when he arrived at the central bank in 2000.
Interest rates are likely to hit 5% within a decade, according to the outgoing Bank of England deputy governor for monetary policy. Sir Charlie Bean said it would be "reasonable" to expect borrowing costs to return to pre-recession levels in the long term - between five to 10 years.
Homeowners have enjoyed a historically low 0.5% base rate for five years but the level has caused misery for savers. Sir Charlie told Sky News: "It might be reasonable to think that in that long term you would go back to 5% but it's probably quite a long way down the road."
Earlier this week, Bank of England governor Mark Carney urged people to focus on the "big picture" rather than obsessing about when interest rates will start to rise.
It followed accusations that he had been behaving like an "unreliable boyfriend" by hinting at a rise this year, before appearing to back-pedal.