Of the six Labour MPs who rebelled and voted with the government on Saturday, only one, Caroline Flint, is standing again in the next general election. But in her constituency of Don Valley, which she has represented for 22 years, that decision seems unlikely to be a costly one.

Explaining her decision, Flint revealed a stark statistic: in the mining villages in this part of South Yorkshire, she wrote in the Sunday Times, 80% of voters backed leave in 2016 (over the whole constituency the figure was 68%). Parliament has not been listening to these people, she wrote: “The voices in our mining villages remain unheard, despite their support for Labour over many decades.”

In Denaby Main, the most deprived of all the pit villages in Don Valley, where a three-bed terrace can cost about £80,000, Flint’s move was warmly received by voters on both sides of the debate. At the Dearne Valley leisure centre, built on top of the colliery after it was filled in back in 1986, Bob Davis broke into superlatives at the mere mention of her name.

Denaby Main in the Don Valley constituency, South Yorkshire. Photograph: Christopher Thomond/The Guardian

“I think she’s wonderful. Absolutely wonderful. She has listened to her constituents, it’s as simple as that,” said the 75-year-old, who set up his own engineering firm after his father forbade his son following him down the mine. Davis, who voted remain “to keep my children happy”, would vote out now: “It would be an insult to me to run a second referendum. I believe strongly in democracy.”

Waiting for his children to finish swimming, Andrew Hampson, 42, said he too voted remain but thought the UK should now probably leave the EU. A former advertising executive who swapped his City job to move to Yorkshire and become a cabinet maker, he thought the remain lobby were still scaremongering. “It’s like with the Y2k crisis,” he said, referring to the experts who warned that a computer bug was projected to create havoc at the beginning of the year 2000. “I just don’t think it’s going to be a disaster.”

Yet he questioned exactly what Boris Johnson’s deal really meant: “I think he’s left it purposefully vague. I do worry what Boris has agreed and I think it’s nowhere near what a lot of people wanted.” Many people wanted a real change in immigration policy, he said, particularly in the former coalfields in the north of England: “I know plenty of liberal Guardian readers who will disagree, but the only reason for having immigration is to keep labour costs down. Working people get castigated for saying that, but it’s true.”

Plasterer Martin Lawton at Denaby Main in South Yorkshire. Photograph: Christopher Thomond/The Guardian

At the Lord Conyers pub in neighbouring Conisbrough, 32-year-old plasterer Martin Lawton said he voted leave, partly to regain border control. “It seems to have been quite easy for people to come in illegally and legally. It should be stricter,” he said, saying that he charges £15 an hour but had been undercut by eastern Europeans happy to work for the minimum wage.

Though she campaigned for remain in the referendum, Flint has become increasingly outspoken against the EU. “When it comes to workers’ rights, the EU isn’t God,” she told the Commons on Saturday. “The fact is local authorities up and down the UK have to outsource contracts to the European Union at the detriment of workers in their local communities. We have seen a rise of zero-hours contracts and poor conditions partly because of that outsourcing.”

Badmouthing the EU is unlikely to lose her many votes. A petition to deselect Flint gained just 178 signatures and she was reselected by her constituency party last week. But her seat is not safe: her majority fell to 5,169 at the last election, down from 14,659 when she was first elected in the 1997 Tony Blair landslide. And in the 2019 European elections, the Brexit party topped the poll in Doncaster with 30,016 votes, with Labour a distant second on 11,393.

Colin Rufus of the Stars in Our Eyes charity. Photograph: Christopher Thomond/The Guardian

But Flint cannot count on the support of all leave voters in her constituency. Colin Rufus, who helps run Stars in Our Eyes, a charity that puts on talent shows, said he would now vote remain: “We were lied to. I voted on the understanding that however many millions each week would go to the NHS. And no one told me there would be a border in Ireland.”

Flint should be campaigning for another referendum, he insisted. “As far as I’m concerned, she voted against what Labour people want. We want another go at it.”