The Bank of England - which ran the tests - said it planned to make banks hold as much as £10 billion ($15.1 billion) in extra capital as the credit cycle begins to normalize.
The scenario which the banks were expected to be able to withstand as part of the test, included an emerging markets-led downturn, with China's gross domestic product declining to an annual rate of 1.7 percent, followed by a fresh euro zone crisis, deflation and recession.
Last year, the Co-Operative Bank was the only U.K. bank to fail the tests, while state-backed Lloyds Banking Group and RBS came close to missing the capital levels set under the stress tests.
Ewen Stevenson, chief financial officer of RBS, said in a statement: "We are pleased with the progress we have made relative to the 2014 stress test, but recognize we still have much to do to restore RBS to be a strong and resilient bank for our customers."
The Bank of England also said on Tuesday that U.K. banks' capital requirements wouldn't continue to rise, signaling an end to the post-credit crisis era of increased caution.