It comes after Theresa May announced a legally binding agreement to end the UK's contribution to climate change in just over 30 years.
Achieving net zero emissions would mean balancing modest carbon emissions produced by absorbing an equivalent amount from the atmosphere by planting trees or other means.
The Climate Change Committee - an independent statutory body established to advise the government on emissions - called for the target in May.
It estimated the cost of doing so at 1-2% of GDP - around £20bn to £40bn - per year.
Taxpayers would bear some of these costs while others would be paid for by homeowners making their houses greener or businesses adapting their practices.
Asked whether they would support the government raising taxes to fund its promise, slightly more Britons were against it than in favour.
Some 36% backed the move while 41% opposed it.
Others were unsure, with 13% answering "neither" and 10% responding with "don't know".
Funding the £20bn to £40bn through increased government borrowing was even less popular - 27% supported it, with 45% opposed (15% said "neither" and 12% "don't know").
The public are even more hostile to finding the money by cutting other public services.
Just 8% would support doing so to eliminate carbon emissions, with 74% opposed (6% "neither" and 12% "don't know").
The move from the outgoing prime minister means the UK is set to become the first G7 country to legislate for net zero emissions, with other countries expected to follow.
A review will take place within five years to assess whether other countries are taking similar action and make sure British industry is not facing unfair competition.
Sky Data interviewed a nationally representative sample of 904 Sky customers by SMS on 12 June 2019. Data are weighted to the profile of the population. Sky Data is a member of the British Polling Council and abides by its rules.
For full Sky Data tables, please click here.