Iain Banks is one of 40 signatories on the letter
The author Iain Banks, together with a group including MPs and church leaders, has accused the government of "writing a blank cheque" for rescued banks.
In a letter to the chancellor, the group said the Treasury had not pushed Royal Bank of Scotland (RBS) to support sustainable investments.
The Treasury said that the conduct of banks was closely monitored.
RBS, which received a government bail-out last year, said sustainability "is something we strive towards".
The group's letter said: "We believe that the Treasury is failing to push the recapitalised banks towards supporting the investments our country needs, and ignoring how the banks are choosing to spend public money.
"In doing so, the government has effectively written a blank cheque with taxpayers' money to the banks to finance anything from destructive fossil fuel companies driving climate change, to hostile takeovers that threaten UK jobs."
It is believed that the group is angry that RBS continues to finance loans to oil and gas companies, while the "hostile takeovers" mentioned, refers to reports that RBS supports US food giant Kraft's bid for British confectioner Cadbury.
The group also called on the government to transform RBS into a "Royal Bank of Sustainability".
Mr Banks is one of 40 members of the group, led by the campaign body the World Development Movement.
Others signatories include the Labour MP Alan Simpson, Reverend Ian Galloway, the convenor of the Church of Scotland, Gordon Roddick, who co-founded the Body Shop with his late wife Dame Anita Roddick and Billy Hayes from the Communication Workers Union.
RBS said: "We have been a leading arranger of finance to the renewable energy sector.
"We only provide project finance to projects which meet the environmental and social standards specified by the Equator Principles."
The Equator Principles is a voluntary initiative for financial institutions that lays out environmental and social guidelines for project financing.
A spokesman for the Treasury said: "The government didn't save the banks for their own sakes but to avert the devastating consequences their collapse would have had on depositors, businesses and the wider economy.
"While the banks operate at arms length on a commercial basis, their conduct is closely monitored through the government's shareholding body UKFI."