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.
They urged the chancellor to impose VAT reductions to encourage energy efficiency, the use of recycled materials and repair services.
The EAC also urged the government to begin scoping work on a carbon tax. That call was backed on Wednesday by a green organisation, the Zero Carbon Campaign.
The UK currently runs several taxes that affect carbon emissions, including Air Passenger Duty, the landfill tax and car tax.
The campaign asks the chancellor to simplify the “inconsistent” pricing system by placing a charge on every tonne of CO₂ emitted in the UK. Proceeds should be used to shield the poorest from the tax changes, it said.
The group believes this will trigger a transition to a clean economy by ensuring that individuals, businesses, manufacturers and policymakers choose less-polluting options.
The Treasury has been examining the relationship between tax and the environment, including a carbon tax. It has also been looking at a pay-as-you drive scheme for motorists to compensate for the loss of cash from petrol taxes as vehicles go electric.
Recent media reports suggest that officials may be moving away from the carbon tax proposal.
The Treasury will not discuss tax changes until the Budget, while the Bank of England declined to comment when it was approached by BBC News.