The poll surveyed 1,507 adults between September 22 and 25.
While Labour still has a lead of 16 points, this is a significant drop of eight points from the last poll by Deltapoll - which saw Labour's lead sit at 24 points.
WATCH NOW: Sunak unveils new approach to net zero
The swing came after Sunak unveiled a bold new approach to tackling climate change, watering down many of the Government's eco-policies.
The Prime Minister used his speech to promise to bring an end to "heavy-handed policies", including taxes on eating meat and forcing voters to install expensive insulation.
The speech saw him herald a new approach to tackling climate change, warning: "We risk losing the consent of the British people” for net zero policies.
He said the UK is "proud to be a world leader in reaching net zero by 2050 - but we simply won't achieve it until we change".
The Prime Minister said the new approach will be "more realistic" and "ease the burden" on families.
He said: "In a democracy, this is the only realistic path to net zero.
"Consent, not imposition. That's how we'll turn the challenge of net zero into the greatest opportunity and the greatest achievement of our life time."
Sunak added: "We are going to change the way our politics works."
But he ruled out holding a referendum on net zero, saying: “I think everyone’s had enough of referendums, quite frankly. But I think the principle of consent is important... We’re going to get to net zero but we’re going to do it in a fair and proportionate way.”
Asked by GB News how much money the measures would save ordinary people, Sunak said it would save families "thousands of pounds".