John Flesher, deputy director of the Conservative Environment Network, said: "The prime minister is right that we need to bring people with us on the road to net zero.
"Expecting too much from households could undermine the country's current consensus on the need to act on climate change."
In the same week Labour made climate action a key part of its pitch to voters, Mr Flesher added: "Conservatives cannot afford to lose their grip on the net zero narrative and must present a compelling, market-based route to net zero."
As the issue that remains popular with voters, the PM should "harness the party's environmental reputation to help build a popular and positive narrative going into the next election and not allow Labour to dominate this issue", Mr Flesher said.