On Friday Moody's Investors Service stripped Britain of its coveted triple-A rating by one notch. The state owns 82 percent of Royal Bank of Scotland and 41 percent of Lloyds after stepping in to rescue them during the financial crisis.
Since then, the banks have shifted their focus to more traditional lending and away from the high-flying, more risky trading that got them into trouble.
"The reality is that the total level of senior bond issuance from all the UK banks has been declining as they shrink the non-core and increase deposits within the mix, so the direct impact is pretty limited," one of RBS's 10 largest shareholders, who declined to be named, said.
RBS has shed around 700 billion pounds ($1.1 trillion) in assets in the wake of the financial crisis, while Lloyds has targeted the sale of 200 billion pounds worth of unwanted loans and investments.
Helping that shift, the Bank of England's Funding for Lending Scheme allows lenders to access cheap funding for making loans to small businesses and households and has reduced their need to tap wholesale funding markets.
Investors also cited prospects for new laws that would ring-fence deposits held by individuals and small businesses from riskier activity, so that they are unaffected if the risky side of a bank fails, putting less pressure on the government to jump to the rescue.
"In theory, this should reduce the correlation between banks and the sovereign," said Andrew Coombs, an analyst at Citi.
EVEN MORE VULNERABLE TO ECONOMY
The fortunes of RBS and Lloyds are becoming more closely linked to the British economy, however, as they retrench from overseas markets. "The risk remains that economic conditions could deteriorate more severely, leading to reduced levels of activity and higher impairment losses," Coombs said.
Lloyds Chief Executive Antonio Horta-Osorio has warned of a "long and difficult recovery" for the British economy.
James Carrick, an economist at Legal & General Investment Management, said Britain's banks were already rated three notches below the sovereign, so he is not expecting an automatic follow-up change in their ratings.
"This downgrade is bad news for the government, because they are going to have to reconsider the fiscal tightening they are going to have to do, but I wouldn't have expected a massive shock to the funding costs of banks at this stage," he said.
Moody's has an negative outlook on both banks, meaning that future downgrades are possible.
At the close of trading on Monday, shares in Royal Bank of Scotland were up 2.8 percent, boosted by news the bank plans to sell off part of its US business, while Lloyds Banking Group was up 0.1 percent.
Markit, a firm that provides data on financial markets including credit derivatives, said the downgrade had already been factored in and the constraints on Britain's growth prospects were already well known.
"This captured lots of headlines, but had a negligible impact on stock and credit markets. The downgrade was more or less priced in," it said.
On the bond markets, the European subordinated financial index was 9 basis points tighter at 246 basis points and the senior financials index was 4 basis points tighter at 146.5 basis points.
"We don't expect any ratings impact from the UK downgrade," a bank analyst said. "In countries like France where the sovereign has been downgraded, we've seen covered bonds issued by the country's banks maintain their triple-A rating, which shows that in some cases investors are more comfortable with bank debt than government bonds."
Moody's changed its outlook on the UK to stable after the downgrade, meaning any further change is unlikely for the next year or so. Standard & Poor's and Fitch still have the country on a top-notch rating but their outlook is negative.