The ratings agency has also changed its outlook for the UK banking system from stable to negative.
Moody’s expects the result of the EU referendum to “reduce the profitability” of the banks.
The outlooks for Barclays, HSBC, Santander, Coventry Building Society, Leeds Building Society, Nationwide Building Society, Nottingham Building Society and TSB Bank have been reduced from stable to negative.
Outlooks for RBS, Skipton Building Society, West Bromwich Building Society and Yorkshire Building Society were maintained because “Moody's believes that the potential impact of the referendum result on these institutions is outweighed by more firm-specific credit considerations”.
The ratings on all 12 of the banks were unchanged.
"We expect lower economic growth and heightened uncertainty over the UK's future trade relationship with the EU to lead to reduced demand for credit, higher credit losses and more volatile wholesale funding conditions for UK financial institutions,” said Laurie Mayers, an associate managing director at Moody's.
“This will be negative for banks' credit fundamentals, as reflected in today's rating actions. Simultaneously, we have changed the outlook on the UK banking system to negative from stable.”