Their situation has been made far worse because other banks have been closing ranks and refusing to take their business.
More than 40 embassies, consulates and High Commissions have been affected.
Even the Vatican has been given its marching orders.
One diplomatic source said he believed HSBC feared being exposed to embassies after it was fined $2billion (£1.32billion) by US authorities last year.
It was blamed for alleged money-laundering activities said to have been conducted through its Latin American operations by drug cartels. HSBC admitted at the time that it had failed to effectively counter money laundering.
Bernard Silver, head of the Consular Corps, which represents consuls in the UK, said: ‘HSBC’s decision has created havoc. Embassies and consulates desperately need a bank, not just to take in money for visas and passports, but to pay staff wages, rent bills, even the congestion charge.’
Embassies also have to pay for ambassadorial accommodation and sometimes even school fees for diplomats’ children.
None of these bills can be settled without a valid British bank account.
John Belavu, minister at the Papua New Guinea High Commission, said: ‘We’ve been banking with HSBC for 22 years and for them to throw us off in this way was a bombshell.’
Lawrence Landau, honorary consul of Benin, said: ‘We have been trying everyone, but all the UK banks are clamming up.’
Other embassies are equally fraught. One said: ‘HSBC did not give us any real explanation. They have only given us until the middle of August to find another bank. We can’t find one and we are going crazy.’
HSBC, however, claims its decision is part of an assessment of all business customers to see if they satisfy five criteria – ‘international connectivity, economic development, profitability, cost efficiency and liquidity’.
One diplomat said: ‘We don’t even know what these criteria mean.’
HSBC would not explain the requirements to The Mail on Sunday and merely 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.’
The Foreign & Commonwealth Office said it was in contact with HSBC and had provided a number of diplomatic missions with letters of introduction ‘to help in opening a new bank account’.
The debacle comes as HSBC prepares to unveil its half-year profits tomorrow.
The group is expected to report that it made $14.6billion (£9.6billion) in profits for the first six months of the year.
It made $12.7billion in the same period last year.