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 U.K.'s first public stress tests were billed as a watershed moment for the British banking industry, which has struggled through six years of balance sheet restructuring following the financial crisis.

U.K. bank shares rallied on the news that only one lender--the Co-operative Bank--had to present new plans to strengthen its balance sheet. Part state-owned Royal Bank of Scotland Group PLC and Lloyds Banking Group squeaked through the test but have already put in place sufficient plans to raise their capital levels, the U.K. regulator said.

Bank of England Governor Mark Carney said the test showed that British banks were "significantly more resilient" than last year. But analysts questioned the relevance of the exercise which focused largely on modeling the effects of a domestic housing crash. On Tuesday Bank of England policy makers were quizzed about a new set of investor concerns: the impact of falling commodity prices and a slowdown in emerging market growth--a factor that could weigh heavily on Asia-focused HSBC Holdings PLC and Standard Chartered PLC.

"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.

With the effects of the financial crisis ebbing, U.K. regulators hailed an annual stress test as a good way to judge its vast banking sector's robustness.

For the first such test, the central bank's Prudential Regulation Authority put eight U.K. lenders through a hypothetical three-year economic collapse where interest rates rise sharply, U.K. gross domestic product falls to 3.5% below its fourth-quarter 2013 level and commercial real-estate prices slump 30%. To pass the test banks had to maintain a 4.5% ratio of capital to risk adjusted assets throughout the period.

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. RBS eked through with a capital ratio of 5.2% and would have normally been asked to submit a revised capital plan, the PRA said. However, the 80% state-owned lender already agreed a new restructuring plan with the PRA this year. Lloyds, which passed with a ratio of 5.3%, is generating capital and so doesn't need to provide a new plan either. The Co-operative Bank flunked the test and agreed to further shrink its mortgage book, the PRA said.

HSBC and Standard Chartered were the two strongest performers. Given the test's U.K. focus, "internationally-oriented UK banks not surprisingly do better," analysts at Citi wrote in a note. The PRA test included the scenario of a global economic contraction already used in an EU-wide test in October, but didn't specifically assess banks' emerging-market loan books. This was despite the fact that lenders, including Standard Chartered, are facing rising bad loans following a commodity price crash.

The British banks broadly welcomed the stress test results and some announced asset sales. RBS said it sold an Irish real-estate portfolio for GBP1.1 billion ($1.72 billion), while Standard Chartered announced its biggest asset disposal in years, with the sale of its PrimeCredit consumer finance units in Hong Kong and Shenzhen.

The Bank of England acknowledged that the stress-testing system is still a work in progress. The central bank raised questions about the banks' ability to crunch a large amount of data for the test. It also said banks need to do more to ensure they correctly evaluate the riskiness of their assets and have the infrastructure and personnel to work on the tests.

It also criticized some of the bankers' willingness to interact with the regulator. "Answers to queries from Bank staff were often incomplete and, in a number of instances, the nature of the interactions fell below the standards set out in the Discussion Paper," the Bank of England said in the results.

The U.K. regulator has yet to adopt the U.S. stress test model, where banks are penalized if they fail to correctly compile data. "As time goes on we may become a little less tolerant," said Mr. Carney.

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

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