The banks involved insist the decision to downgrade their credit status made by rating agency Moody's is not a problem.

Two major UK banks – the Royal Bank of Scotland and the Lloyds TSB division of Lloyds Banking Group – and 10 smaller banks and building societies, had their ratings cut yesterday. But all insist they are in good health and well-capitalised.

Chancellor George Osborne insists the decision was long-expected and triggered by the Government's own actions.

Even Moody's was downplaying the importance of the change. The Government has signalled a clear shift in responsibility, by transferring liability for any future bail-outs needed so that shareholders – rather than taxpayers – carry the can. This affects any bail-outs of major banks, Moody's said, and the new ratings of smaller institutions reflect the fact that the UK Government is now more likely to let them fail if they become "financially troubled".

But even if the Government wanted to bail out the banks in future, the country probably cannot afford to do so. Therefore it is right to say the downgrading has largely been acknowledged already by the market and the impact on the costs of funding for the institutions affected should be minimal.

However this did not stop shares in UK banks falling yesterday – including shares in Barclays, whose rating was untouched by the Moody's changes.

Even if the downratings were merely a confirmation of an adjustment already made by the markets, the decision – and yesterday's parallel announcement of a similar downgrading of Portuguese banks – contributes to confidence, or a lack of it. That is more bad news at a time when bad tidings from the markets seem relentless. Also yesterday, the agency Fitch's announced it was downgrading Spain's credit rating.

One significant impact of the move by Moody's will be on savers. Already smarting over the quantitative easing measures, which will keep interest rates low at a time of higher inflation, many will feel even more exposed at this news from Moody's.

Should a bank or building society fail, most savers will be protected by the Government-backed Financial Services Compensation Scheme.

But there are still many who see the agency's mass downgrading as a serious over-reaction and, if it damages confidence to the extent of triggering particular concerns about any financial institution, it is one which could cause serious harm.

The other spectre is over the potential need to further bail out RBS, if the trouble in the eurozone leads to a need to recapitalise Europe's banks. Should a decision be taken that this is necessary, UK-based banks could come under pressure to do the same.

The UK Government was already concerned about the need to revisit the bank, which has been the beneficiary of the world's biggest ever bail-out at a £45 billion cost to the taxpayer.

Moody's actions yesterday did nothing to allay that concern.