By Max Colchester and Margot Patrick 

The Bank of England on Tuesday said all but one of the U.K.'s major banks passed a balance sheet health check but warned that two of the nation's biggest lenders needed to improve their capital levels.

The central bank's Prudential Regulation Authority put eight U.K. lenders through a hypothetical three-year economic collapse. To pass the test banks had to maintain a 4.5% ratio of capital to risk adjusted assets throughout the period.

Only one bank, the Co-operative Bank, needed to submit a revised plan to strengthen its balance sheet. Part state-owned Royal Bank of Scotland Group PLC and Lloyds Banking Group only narrowly passed the test but have already put in place sufficient plans to raise their capital levels, the PRA said.

The test stressed the eight biggest U.K. lenders including HSBC Holdings PLC, Barclays PLC, Royal Bank of Scotland Group PLC, Lloyds Banking Group PLC, Standard Chartered PLC, Santander UK, Nationwide Building Society and The Co-operative Bank.

RBS, which passed with a capital ratio of 5.2%, would have normally been asked to submit a revised capital plan, the PRA said. However, the 80% state-owned lender already agreed a restructuring plan with the PRA this year so a new plan wasn't required. Lloyds, which passed with a ratio of 5.3%, is generating capital and so doesn't need to provide a new plan either. But it is unclear whether Lloyds would get approval from the regulator to restart its dividend payments.

Lloyds, which has said it aims to resume paying dividends this year after a six-year hiatus, has already made "significant progress" on the year-end 2013 figures used for the test, Chief Executive António Horta-Osório said.

RBS Chief Financial Officer Ewen Stevenson said the bank has made good progress this year, although "there is still much work to be done to improve the resilience of our balance sheet." The bank also announced the sale Tuesday of an Irish real-estate portfolio for GBP1.1 billion ($1.72 billion), adding to a series of asset disposals that have helped halve the size of its balance sheet since 2008.

Tuesday's health check marked the first public stress test of the U.K.'s banks by the Bank of England. It built upon European Union-wide stress tests in October, and reflected improvements in British banks' capital positions since the financial crisis triggered a multi-hundred billion pound government bailout.

"The results show that the core of the banking system is significantly more resilient, that it has the strength to continue to serve the real economy even in a severe stress, and that the growing confidence in the system is merited," said Bank of England Governor Mark Carney.

Yet some analysts said the test didn't go far enough in assessing banks' ability to withstand global shocks such as the recent commodities rout, and gave only a limited assessment of emerging-markets focused HSBC and Standard Chartered.

"The Bank of England has clearly flagged a bunch of macro risks that are playing out today that were not central to the stress tests done this year," analysts at Sanford C. Bernstein said in a note.

The stress test saw interest rates rise sharply to 4%, U.K. gross domestic product fall to 3.5% below its fourth-quarter 2013 level, unemployment peak at 12% and commercial real-estate prices slump 30%. The regulator had previously warned that if banks only just pass the test, they could still be required to take action to bolster their balance sheets.

The Co-operative Bank already flagged that it would probably fail the balance-sheet check. The PRA on Tuesday said that the Co-op registered a capital ratio of -2.6% after the test. The Co-op Bank is working through a restructuring plan agreed with the regulator following a bailout by bondholders and has agreed to further shrink its balance sheet in particular cutting its mortgage book, the PRA said. The bank will cut risk adjusted assets by GBP5.5 billion--or more than one third of its adjusted assets--by the end of 2018.

Co-op Bank Chief Executive Niall Booker said the test failure wasn't a surprise and that the bank is on its way to getting stronger.

Bank regulators across the world have increasingly applied stress tests since the financial crisis exposed serious weaknesses in domestic and international banking supervision. The Bank of England said it was largely satisfied with the stress test process but that banks will need to do more in the future to make sure they are providing accurate data and have the infrastructure and personnel to work on the tests.

The balance sheet check will form the basis for annual U.K. bank stress tests. The PRA previously said it would broaden the tests to include U.K. arms of foreign banks, but on Tuesday said the 2015 test will be limited to the same eight banks.

Write to Max Colchester at max.colchester@wsj.com and Margot Patrick at margot.patrick@wsj.com

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