Lloyds Banking Group and Royal Bank of Scotland Group are among the lenders who have had their debt ratings put on review ahead of a possible cut.
Other major institutions highlighted include Santander UK and the customer-owned Nationwide Building Society.
The ratings agency said, however, that the outlook on Barclay's senior debt and deposit ratings had gone from negative to stable.
Elisabeth Rudman, a senior credit officer at Moody's, noted the reassessment came following guidance from UK authorities that suggested "banks that fail in the future should not expect capital injections from the public purse".
She added the move was not driven by reductions in the strength of the banking system or the government.
Last week, Moody's downgraded six banks in Denmark, after failings at regional lender Amagerbanken led to the European Union's first senior credit losses.
By Tony Aynsley