Louise Richards, director of policy and campaigns at the institute, said she would ask Paul Smee, the head of the council, to consider alternative payment options and to consult more widely with representatives from charities over the issue.
She said the proposal by the Payments Council to phase out cheques could give the green light to banks to stop using them before its specified date of 2018.
The institute has also asked its members to lobby their local MPs and to contact the Payments Council directly over the matter.
Richards said: "Many charities that rely on an older supporter base receive more than 70 per cent of their income by cheque. These charities have expressed real fears that those who currently donate this way might stop giving altogether if they are no longer able to do so by cheque.
"There has been insufficient consultation on this move, which has seemingly been designed entirely as a cost-cutting measure for the banks. We believe there has been scant consideration of the disastrous effect this could have on charitable income."
A spokeswoman for the Payments Council said: "We are currently meeting as many charities as possible to discuss the issues raised by plans to withdraw the cheque in 2018, so that we can ensure suitable alternatives are in place to meet their needs.
"We recognise that many charities are highly dependent on cheques, but are aware that this can often be due to a lack of suitable alternatives. Our work will involve finding alternatives that meet the needs of the charity, help them to function more efficiently and prove acceptable to those who make charitable donations by cheque."
The meeting will take place on 5 February.