MOST Banks!? That is not true. SOME Banks is more accurate.
They do NOT accept:
Bank of Scotland
Bank of Ireland
Metro Bank (they only provide services to Business Accounts not Personal Accounts)
First Trust Bank
Allied Irish Bank
Marks and Spencer
Deutsche Bank UK
Nationwide and 43 other building societies
and dozens (30 or 40) of various Indian, Arabic, Greek, Cypriot, American, French and Asian banks operating in the UK, small independent Private banks and various Private Banking arms of larger banking groups.
This list also excludes various electronic money firms such as Monese etc who also do not use the Post Office.