Moody's says it could cut its ratings of 19 UK banks to reflect the lower chance of a future government bail-out.
Smaller lenders, including building societies, would likely be the first to face cuts, the ratings agency, according to the BBC.
The big four banks, which are seen as the most systemically important because of their size, will be assessed in H2 this year.
"Systemic support" means the banks currently enjoy ratings up to five notches higher than they would otherwise.
Before the crisis, the maximum such support assumed was two notches for the biggest banks, implying some could see their credit ratings cut by three notches.
Any such downgrade is likely to increase a bank's cost of borrowing, because many investors are restricted from lending to borrowers with lower ratings.
"This reassessment could trigger negative outlooks, reviews for possible downgrade, or downgrades for some ratings, and will be taking into consideration Moody's expectations on how the relevant banks' standalone credit strength will develop," the rating agency says.
The reassessment is due to the changing regulatory environment, which Moody's believes will reduce the chances of UK banks enjoying financial rescues from the government in the future.
It did not reflect any deterioration in the banks' performance on the financial strength of the UK government, Moody's says.
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