Although Barclays and RBS fell below the minimum capital level requirements in the stressed scenario, the BoE said the two banks had "significantly" improved their capital positions since the end of 2016.
The central bank ruled however that the nation's seven top retail banks must hold another £6.0 billion ($8.0 billion, 6.7 billion euros) in combined capital reserves to safeguard against crisis.
Britain's banks could cope with a "disorderly" Brexit without needing to curb lending or be bailed out by taxpayers, the Bank of England said on Tuesday after carrying out its annual health check on lenders.
"The stress-test scenario ... encompasses a wide range of United Kingdom macroeconomic risks that could be associated with Brexit", read a statement from the BoE's Financial Policy Committee (FPC).
Britain is due to leave in March 2019 but negotiations with Brussels over the post-Brexit relationship have failed to make much progress, raising fears that tariffs and other restrictions would be slapped on British exports to the EU.
The stress assessments were created to see whether the banking sector can weather a fierce worldwide recession, crashing house prices and soaring unemployment.
While concluding that lenders can deal with Britain crashing out of the European Union without a deal and restrictions imposed on British business, the Bank of England warned that additional problems may emerge if a "disorderly" Brexit takes place at the same time as a sharp global recession.More news: Sadio Mane plays down incident with Jurgen Klopp
Governor Mark Carney said the Bank's Financial Policy Committee was "taking action to ensure the financial system is resilient to a very broad range of risks so that the people of the United Kingdom can move forward with confidence that they can access the financial services they will need to seize the opportunities ahead".
That will give Britain's retail lenders combined capital reserves of £11.4 billion.
The central bank today revealed the results of its annual round of stress testing on the likes of Barclays, Royal Bank of Scotland, HSBC and Lloyds Banking Group.
The 2017 tests examined banks' ability to withstand a downturn worse than the one experienced following the collapse of Lehman Brothers in 2008.
The Bank said that this was the first year since it started conducting the test in 2014 that none of the big banks would need to strengthen their capital positions as a result of the outcome.
"The 2017 stress test shows the United Kingdom banking system is resilient to deep simultaneous recessions in the United Kingdom and global economies, large falls in asset prices and a separate stress of misconduct costs", the Bank of England said.