HSBC has written to one of London's biggest mosques at Finsbury Park and other organisations, including an Islamic think tank, saying that to continue providing services would be outside the bank's "risk appetite".
It said decisions to close accounts were "absolutely not based on race or religion".
The bank's statement said, "We do not discuss relationships we may or may not have with a customer, nor confirm whether an individual or business is, or has been a customer.
"Discrimination against customers on grounds of race or religion is immoral, unacceptable and illegal, and HSBC has comprehensive rules and policies in place to ensure race or religion are never factors in banking decisions," it said.
Khalid Oumar, one of the trustees of Finsbury Park mosque, questioned the motives behind the letters.
"The letters that have been sent and the letters that we received do not give any reason why the accounts were closed in the first place," he said.
"That has led us to believe that the only reason this has happened is because of an Islamophobic campaign targeting Muslim charities in the UK," he added.
Until 2005, the mosque was run by Abu Hamza, who in May this year was convicted of terrorism offences in the US.
"The positive work we have done since taking over from Abu Hamza to change the image of the mosque, there is nothing really that can explain (HSBC's decision)," mosque chairman Mohammed Kozbar told the BBC.
In December 2012, HSBC had to pay US authorities USD 1.9 billion (1.2 bn pounds) in a settlement over money laundering, the largest paid in such a case.
It was alleged to have helped launder money belonging to drug cartels and states under US sanctions.
In August last year, it was reported that HSBC asked more than 40 embassies, consulates and High Commissions in the UK to close their accounts.
At the time, the bank 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".