The Royal Bank of Scotland (RBS) and Standard Chartered have emerged weakest in the Bank of England's stress test.
The banks did not have enough capital strength to meet some of the measures laid down as part of the annual MoT of lenders' capacity to deal with financial shocks.
Regulators allowed the banks to pass the overall test after considering steps they had taken to shore up their central reserves and crisis survival strategies.
Meanwhile Barclays, HSBC, Lloyds Banking Group, Nationwide Building Society and Santander UK cleared the assessment.
Governor Mark Carney said the UK lending sector was "already most of the way there" and the results showed banks were "significantly more resilient" today than before the global financial crisis.
The improvement was testament to reforms brought in after the 2008 meltdown that have "have rebuilt capital and confidence in the UK banking system", he explained.
Speaking as the results were published Mr Carney also noted concerns over lending practices in the buy-to-let market, saying the Financial Policy Committee (FPC) will "monitor developments in buy-to-let activity closely."
It is the second year that the Bank of England has put UK lenders through their paces by simulating a major financial crisis.
The FPC's latest assessment of global markets was that growth continued to be sluggish and both emerging and developed markets posed challenges.
This year's stress test used a scenario where Chinese growth stalled dramatically, causing a housing market crisis in China and Hong Kong, plus a collapse in the price of oil to 38 dollars (£25) a barrel.
The model also included a three-year slowdown in Europe and a sharp fall in commodity prices.
In the event of such a seismic shock to the global financial system the Bank predicted profits across the board would fall by £100 billion at their lowest point, the report said.
Meanwhile the banks would lose a total of £37 billion from their central reserves, around two thirds.
It meant shareholders could suffer a £21 billion reduction in their dividends to mitigate the impact on the banks' capital. The cuts would come as a result of either banks' individual policies or a new set of EU rules.
The projections showed RBS, bailed out by the taxpayer in the last downturn, did not meet its individual capital level expected by the regulators in the stress scenario.
However bosses plan to increase its additional capital in 2016, allaying the regulator's concerns.
Standard Chartered did not meet the minimum capital of 6% in its central capital reserve, its multi-use buffer fund, after the stress test was applied.
The Prudential Regulation Authority judged the banks' recent strategy review, plus steps it had taken to shore up its capital position, to be sufficient to let it pass the overall test.
The banks have until 2019 to fulfil the regulator's requirements.
Last year the Co-Operative Bank was also stress tested, although it was left out of this year's modelling while it undergoes restructuring.
Mr Carney said the "elevated" international security concerns, in the wake of the attacks in Paris and amid the worsening situation in the Middle East, had been taken into account when assessing the UK's overall financial resilience.
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