For all the fanfare about UK political parties facing pressure to re-examine their climate policies given the cost of living crisis, voters in two areas near clean air zones support measures to ensure net zero targets are met.

Wrangling in the aftermath of last Thursday’s byelection, when Labour narrowly lost out on winning Uxbridge and South Ruislip, has pushed briefings by some MPs into overdrive about what policies should be reconsidered.

But people who voted Labour in 2019, as well as those who voted Tory, said the row had largely passed them by. During a focus group, convened by More in Common for the Guardian, they broadly backed current commitments to tackle climate change – and in some areas thought the government should go further.

Wildfires on the Greek island of Rhodes struck a chord, but so did last summer’s record heatwave in the UK and other crises across the world, such as floods in Pakistan earlier this month.

“The more I understand it, the more I realise how serious it is,” said Thomas K, a business director in the north London constituency of Chipping Barnet. “The more we live through it, the more real we realise it is – and less about speculation or it being subjective.”

Some ministers have been keen to suggest that net zero pledges are unpopular with voters, given the costs incurred when household budgets are increasingly squeezed. The government announced this week it would delay its flagship recycling scheme by a year.

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However, there was broad support from the focus group of voters in the constituencies of Chipping Barnet and Don Valley, South Yorkshire, for bolder action, with ideas including making solar power panels on new-build homes mandatory and banning single-use plastic.

The voters came from areas affected by the drive to clamp down on polluting cars, with the ultra-low emissions zone in London due to be expanded next month and Sheffield having already implemented a clean air zone.

“The majority of people wouldn’t have to pay that £12.50 on a daily basis,” said Adele of the move to expand ULEZ to include outer London. A 66-year-old carer who voted Tory in 2019, she said: “It is about air quality and things like the population not having to endure asthma and bronchial problems.”

Those in the focus group were happy to change their habits to be more environmentally friendly, but felt held back by high rail fares or a lack of charging points for electric cars.

“My daughter’s three, so any little thing that I can do for the future I think that’s something,” said Shireen, a 40-year-old tutor.

Mona, 48, a mechanic from Don Valley, said she did not appreciate how environmentally minded she was because “we’ve just got used to doing it”, but on reflection said with a smile: “Actually, I am a green warrior.”

For one London resident, the ULEZ expansion in London next month was still a concern. Thomas K said his events firm had a fleet of vehicles and would face a financial hit. He suggested that businesses be exempt from the charge for higher-polluting vehicles.

There were also wider concerns that politicians might only tackle the climate crisis if there was a financial incentive for them. One suggestion made was that politicians were too exposed to vested interests because they undertook second jobs.

“Across the group, the main worry was that politicians either wouldn’t be bold and forward thinking enough to take the long-term steps necessary to reach net zero or would see it as a money-making opportunity.”

The cost of living crisis and the NHS remained the top of the group’s concerns. “I paid £2.80 for a cabbage last week, I nearly fell through the floor,” said Adele. “I still haven’t got over that. And bills? My middle name’s bill.” Wai, a 50-year-old accountant, said his local hospital in Don Valley was “falling to bits”, pushing up waiting times across the region.

Luke Tryl, the director of More in Common, said: “The heated rows over green policy that have dominated Westminster over the past week, had passed voters we spoke to in Don Valley and Chipping Barnet by.

“While this group were largely convinced of the need to take action on climate change and were quick to point to the actions they were already taking, it was when it came to our politicians and political class that they lost faith.

“Across the group, the main worry was that politicians either wouldn’t be bold and forward thinking enough to take the long-term steps necessary to reach net zero or would see it as a money-making opportunity.”