Monetary financial institution
From ACT Wiki
Monetary Financial Institutions (MFIs) are central banks and other institutions whose business is to take deposits and/or close substitutes for deposits from entities other than MFIs and, for their own account (at least in economic terms), to grant credits and/or make investments in securities.
In many contexts, MFIs excluding central banks are considered.
So, for example, the Bank of England publishes statistics under the heading "Monetary financial institutions (excluding central bank) balance sheet".
But conversationally and informally they are taken as relating to "MFIs".