In the letter, Friends of Al-Aqsa urges the bank to re-open the accounts, accusing it of turning its back "on the ethical principles that the Co-operative Bank has strongly stood by for so long".
The NGO says it does not send or receive money from abroad and has not contravened any laws and regulations.
The letter says that the account held by Friends of Al-Aqsa, which has been open with the Co-operative Bank for 10 years, has never been overdrawn nor incurred any penalties.
Friends of Al-Aqsa is one of a number of pro-Palestinian organisations that have had their bank accounts closed by the Co-operative Bank in recent months, including the Palestine Solidarity Campaign.
In a statement, a Co-operative Bank spokesman said the bank did not comment on individual accounts and decisions to close accounts were not statements on the work of NGOs or the causes they supported.
The spokesman said advanced due-diligence checks were required by all banks for customers who operated in, or sent money to, any high-risk locations throughout the world to ensure that funds did not inadvertently fund illegal or other proscribed activities.
"Unfortunately, after quite extensive research, the charities involved did not meet our requirements or, in our view, allow us to fulfil our obligations," a spokesman said.
"This does not mean that we cannot or will not facilitate humanitarian, educational, medical and human rights donations to the Gaza region. Many high-profile organisations do excellent work in these fields in Gaza and elsewhere, and we facilitate regular donations to some of these organisations through our current accounts and credit cards.
"We would like to reassure customers that we apply consistent criteria when dealing with all customers and countries, and this decision is about adhering to our obligations under the law and not about arbitrary decisions or any form of discrimination or inequality.
"We have done considerable research, and this decision is based on our adherence to our legal obligations and on our assessment of risk. Adhering to our obligations is clearly part of our ethics and we continue to support charities in all sorts of areas that can meet our criteria, including charities as stated above that operate in Gaza."