Chancellor Rishi Sunak is being urged to use the Budget to change the financial system to better protect the environment.
One group wants him to impose a carbon tax and use the proceeds to protect the poor from high energy bills.
A second petition is calling for Bank of England rules to encourage banks not to invest in fossil fuels.
Mr Sunak is expected anyway to update the Bank’s mandate to include a greater focus on climate.
But campaigners want the new wording to stop the Bank from supporting fossil fuel firms through schemes such as its £20bn corporate bond purchase programme, which involves buying debt issued by firms such as Shell and BP.
The Bank responded to similar calls in January by saying that it has "an ambitious work programme on climate change, from the stress testing of the largest UK banks and insurers against climate-related financial risks through to working internationally with the central bank network for greening the financial system".
Some campaigners also want the Bank to work with the Treasury in funding a National Infrastructure Bank investing in sustainable industries.
The petition comes from Positive Money, a not-for-profit organisation claiming 65,000 supporters that was set up in the aftermath of the financial crisis and is funded by trusts and foundations.
One campaigner, Hannah Dewhirst, said: “The Bank and the financial system it regulates is currently funding catastrophic climate breakdown, which will again see ordinary people paying the price of bankers’ recklessness."
Anna Vickerstaff, another campaigner for the climate group 350.org, said: “British banks are the worst in Europe for funding fossil fuels.
“Banks operating in the UK are fuelling the climate crisis by financing fossil fuel projects from Argentina to Mozambique.”
The petition comes after MPs on the cross-party Environmental Audit Committee (EAC) last week called on the government to add climate and nature objectives to the Bank’s mandate.