LONDON — News that Britain’s bailed-out banks may have to sell more of their businesses in return for being rescued jangled market nerves Monday, with Royal Bank of Scotland, Lloyds Banking Group and the wider financial sector facing a crucial week in the road to recovery.

Royal Bank of Scotland Plc announced Monday that EU regulators were demanding it sell significant parts of its business, more than it had expected — a move supported by the government, which on Sunday called for a thorough shake up of the sector.

The news caused shares in RBS, which is 70 percent owned by the government, to fall more than 7 percent to their lowest level in more than three months. RBS said it would release details of the asset sales by Friday morning, when it reports third-quarter results.

Lloyds, which is itself 43 percent owned by taxpayers, is expected to announce Tuesday fundraising plans aimed at keeping the government from acquiring a larger stake. It may also update the market on its disposal plans. Shares were down 3.5 percent by midday.

“Uncertainty over the path of economic recovery, combined with a lack of visibility over the potential for further credit losses, means an investment in either RBS or Lloyds remains very high risk, and we would expect both stocks to continue to exhibit a high degree of volatility over the next few days,” said Jonathan Jackson, head of equities at Killik and Co. in London.

“The announcement over the weekend that CIT Group, the U.S. small-business lender, has filed for bankruptcy should also serve to remind investors that the financial crisis is far from over,” Jackson added.

The Financial Times reported that Lloyds would provide more details on Tuesday of its plans to raise up to 25 billion pounds ($41 billion) and stay out of the government’s Asset Protection Scheme for insuring losses on toxic assets. That would prevent the government from becoming the majority shareholders in the group.

The divestitures are being driven by the European Commission, the executive arm of the European Union, which has made this part of the price the banks must pay for their public support.

EU Competition Commissioner Neelie Kroes served notice in June that RBS and Lloyds might have to sell a large chunk of their assets to comply with EU antitrust rules. “The massive aid received by banks such as Lloyds and RBS allows these banks to remain leaders on markets which are concentrated,” she said.

U.K. Treasury chief Alistair Darling on Sunday said all three banks rescued by taxpayer money — which besides Lloyds and RBS includes Northern Rock — would be shedding parts of their businesses.

Media reports say RBS may have to sell its Churchill and Direct Line insurance operations, a large part of its investment bank, and its U.S. banking arm, Citizens Financial Group. The Providence, Rhode Island-based business employs about 24,000 people.

Reports also suggest that Lloyds Banking Group could shed its mortgage arm, Cheltenham & Gloucester, and Intelligent Finance, an Internet bank. Some analysts have even suggested that Lloyds might offload Halifax, the nation’s leading mortgage lender.

“Although we can speculate about what else RBS will have to divest it seems we only have a few days to wait for the definitive answer,” said Nic Clarke, analyst at Charles Stanley & Co.

RBS said it was also close to agreeing with the Treasury about terms for insuring 325 billion pounds ($530 billion) of troubled assets, a step which will increase the government’s stake in the bank from the current 70 percent to more than 80 percent.

Darling said the government sought “quite a substantial divestment — perhaps branches or perhaps particular institutions that they own.”

“Unless we get competition we are going to end up with half a dozen big providers, which would be a big reduction in choice and that would not be acceptable,” he said.

Though Darling spoke of reshaping Britain’s banking industry over three or four years, opposition politicians warned against any fire sales of assets.

“It is obviously right that British retail banking becomes more competitive in order to stop the continual ripping off of customers,” said Vince Cable, economic spokesman for the Liberal Democrat party. “But there’s no justification for a rapid sell off of state assets in the current depressed environment when the taxpayer will get a very poor deal.”

The government announced last week that Northern Rock would be split into a profitable mortgage lender and a second unit holding shakier assets.

“We will be able to split Northern Rock by the end of the year but I’m not going to rush into a sale. We will only sell when the time is right and when the price is right,” Darling said.

Edinburgh-based RBS, founded in 1727, was aggressively acquisitive in the last decade, vaulting into the big time in 2000 with the hostile takeover of National Westminster Bank, then the biggest bank takeover in British history. But it was leading the 48 billion pounds takeover of the Dutch bank ABN Amro at the top of the market in 2007 that proved disastrous. In October last year, at the height of the financial crisis, the government invested 20 billion pounds to keep the company afloat.

Lloyds had been much more conservatively managed when it was Lloyds TSB, but the government waived competition rules and encouraged it to rescue Scotland’s other big bank, Halifax/Bank of Scotland, during the global crisis.

RBS reported a 1 billion pounds loss in the first half of the year, while Lloyds said it lost 3.1 billion pounds in the first half. Northern Rock lost 1.25 billion pounds.

In contrast, two big rivals which avoided government bailouts reported profits: 3.35 billion pounds at HSBC and 1.89 billion pounds at Barclays.