Prime Minister Rishi Sunak and Labour leader Sir Keir Starmer have been urged not to ditch their parties' green policies, as a Cabinet minister said environmental reforms being placed on landlords were "asking too much, too quickly".
London mayor Sadiq Khan's expansion of the ultra low emission zone (Ulez) has been blamed on Labour failing to take Boris Johnson's old seat of Uxbridge and South Ruislip, with the Conservatives hanging on by 495 votes.
Sir Keir has vowed to stick with his green pledges, but said the party would need to reflect and "learn the lessons" over how they are implemented.
The development comes as Housing Secretary Michael Gove said he wants to "relax" the deadline for landlords in the private rented sector to make energy efficiency improvements to their properties.
He told The Sunday Telegraph the proposal to ban landlords from renting out their homes unless they pay to increase the energy performance certificate rating of their properties should be pushed back past 2028.
The upgrade required to increase a property's energy performance could include fitting a heat pump, providing insulation or installing solar panels, which the newspaper suggested could cost thousands of pounds.
Mr Gove said: "My own strong view is that we're asking too much too quickly."
Separately, he also warned about "treating the cause of the environment as a religious crusade" as he called for "thoughtful environmentalism".
With the result in Uxbridge a rare bright spot in Thursday's set of three by-elections, the prime minister has come under renewed pressure to water down commitments designed to help the UK meet its pledge of having a net zero carbon economy by 2050.
Tory MP Craig Mackinlay, chairman of the Net Zero Scrutiny Group, has suggested delaying the ban on new petrol and diesel cars, pushing it back "at least" five years to 2035.
Mr Gove, who was environment secretary when the 2050 net zero pledge was made during Theresa May's premiership, said he did not know whether the car-ban deadline was "perfectly calibrated" but said it was "achievable".
Health minister Maria Caulfield on Saturday avoided questions probing whether policies, such as the phasing out of gas boilers by 2035, should be postponed.
Senior environmentally-minded Tories have urged both their own party and Labour not to drop green policies in the hope of short-term electoral gains.
Alok Sharma, the former president of the COP26 climate summit in Glasgow, tweeted: "Given the economic, environmental and electoral case for climate action it would be self-defeating for any political party to seek to break the political consensus on this vital agenda."
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Baron Goldsmith of Richmond Park, who resigned as an environment minister in the Foreign Office last month with a scathing attack on Mr Sunak's "apathy" on the matter, said dropping climate change-tackling policies would be "politically suicidal" given their growing support among voters.
"To use these recent results to advocate abandonment of the UK's previous environmental leadership is cynical and idiotic," Lord Goldsmith told The Observer.
For Labour, despite delivering a huge blow to the Tories with a by-election win in Selby and Ainsty, the post-mortem examination has been far more focused on what went wrong in Uxbridge.
The party required a much smaller swing in west London than the 24 percentage points it secured in north Yorkshire to unseat the Tories - the Selby swing was the second largest produced by Labour at a by-election since 1945 - but it came up short against Tory challenger Steve Tuckwell, the newly-elected MP who painted the vote as a referendum on Ulez.
Mr Khan, the Labour incumbent in City Hall, plans next month to widen the £12.50 daily charge for vehicles which fail to meet emissions standards to all London boroughs, taking it beyond the capital's north and south circular roads.
Sir Keir told broadcasters on Saturday: "I don't think there is any doubt that Ulez was the reason that we lost the election in Uxbridge."
He has confirmed he has spoken to Mr Khan about the policy, which currently faces a legal challenge.
According to The Sunday Times, Sir Keir's senior advisers had predicted Ulez could be a vote loser and had spent months urging Mr Khan to scrap the expansion.
Mr Khan's team defended his plan, saying only one out of 10 cars driving in outer London would face the charge, with a £110 million scrappage scheme available to help lower earners to upgrade their vehicles.
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