The aim of the campaign, which launches next month in the national press, is to persuade the government to introduce a climate change bill in the Queen's speech.
The campaign, created by Sheffield agency Dig for Fire, with media planning by Rocket, is part of the bank's "Customers who care" initiative, which asks members to vote on which cause it should support.
For every £100 customers spend on the bank's credit and debit cards, it donates 1.25p to the campaign fund. Previous campaigns have given more than £3m to mental health charities and those seeking the abolition of landmines.
Separately, the Co-operative Group has signed a three-year deal with Scottish Power for its stores to be supplied exclusively with energy from renewable sources.
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