HSBC, the biggest bank in Britain is reported to have given dozens of diplomatic missions in London 60 days to move their accounts elsewhere.
More than 40 embassies, consulates and high commissions are affected.
HSBC said embassies were subject to the same assessments as its other business customers.
They need to satisfy five criteria: international connectivity, economic development, profitability, cost efficiency and liquidity. A spokesman said:
"HSBC has been applying a rolling programme of "five filter" assessments to all its businesses since May 2011, and our services for embassies are no exception.
"We do not comment on individual customer relationships."
The head of the UK Consular Corps told the Mail on Sunday the decision has created "havoc".
The BBC reports the Foreign Office has been in touch with HSBC, to help diplomats open other bank accounts.
The Mail on Sunday reported that the High Commission of Papua New Guinea and the Honorary Consulate of Benin were among those asked to move their accounts within 60 days.
HSBC was fined $US1.92 billion (£1.26 billion) in the United States last year after it was blamed for money laundering activities said to have been conducted through its Latin American operations by drug cartels.
The bank admitted at the time that it had failed to effectively counter money laundering.
The BBC reports embassies are treated like business customers by banks as they generally use services like cash and payroll management and can take out loans.