Area is political bellwether that many believe party must win if it is going to return to government

Their whistlestop canvassing tour of the neat estate of detached 1970s homes in the far north-east of Swindon now complete, Labour’s dozen or so activists wait for the local candidate, Barrie Jennings, to finish one last doorstep conversation with a voter.

As he finally leaves, a colleague asks Jennings what he had been talking about for so long. “The Korean war,” he replies. Jim Grant, the leader of Swindon’s Labour group, looks bemused. “Well, as long as it gets him out voting for us,” he eventually says.

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Labour is, in the words of the Conservative leader of Swindon council, “throwing the kitchen sink” at taking control of the Wiltshire town in the local elections on 3 May, and with good reason.

Swindon is a classic political bellwether area, its parliamentary seat – split into two seats in 1997 – tending for decades to almost exactly track the national election result. With the council, Labour needs to gain four seats from the 18 contested to take control.

As Grant says: “If Labour are ever going to form a national government, we will need to win places like Swindon. This is the start of that push.”

The push has involved Jeremy Corbyn visiting five times in the past six months, while the Momentum group is holding a mass event in the town. Karin Smyth, the Bristol South MP, has caught the train to help out with the lunchtime door-knock in the Lower Stratton area, even though so few people are in she barely gets a chance to speak to anyone.

With Westminster obsessions such as antisemitism within Labour never mentioned, according to Grant, the fight is largely being contested in one area: austerity, or more precisely, how national cuts are affecting local services.

On Corbyn’s last visit, earlier this month, he visited the site where Labour say they would reinstate a Surestart children’s centre – all of these in Swindon have now closed – and Grant argues very few voters are failing to notice the cumulative impact of eight years of cost-cutting.

“I think that message is hitting home, particularly when you have cuts to local government but your council tax is going up by 15% over two years,” he said. “I’m starting to get our own ‘pay more for less’ line quoted back to me on the doorstep.”

Facebook Twitter Pinterest Labour party activists campaigning in Stratton St Margaret. Photograph: Adrian Sherratt/The Guardian

This message clearly resonates with one of the few voters to be found at home, Patricia Hackett. “Anything that’s for the masses, the money’s not there,” she says. “If you want to bomb some other country, there’s always enough money. But new books for a school? No.”

However, the lifetime Labour supporter cheerfully admits she is an exception on her street – she has given up talking politics with her neighbours – and others tracked down by the Labour team have other things on their mind. One man admits to being so busy planning his upcoming wedding he doesn’t even know if he’ll vote.

David Renard, the Conservatives’ leader in Swindon, says his doorstep conversations focus less on cuts, but concedes he does spend much of his time explaining how the council’s statutory obligations in adult and child social care now use up about three-quarters of all its budget, up from less than 50% a few years ago.

“I think people get that,” Renard says. “They don’t necessarily like it, but they do understand they, and we, have a social responsibility.”

Renard is among the many council leaders who argue the way social care is financed is not sustainable: “Successive governments have ducked it. But I think we are now getting to the stage where ducking it really isn’t an option. We do need to have a national conversation about it.

“People accept we pay for healthcare through general taxation, but they don’t see the connection with social care.”

He declines to predict whether his party will hold on to the council, but agrees with Grant that Swindon is precisely the sort of place where an opposition with aims of returning to government should take control.

“If they don’t make any gains – which is a distinct possibility at the moment – then, after throwing the kitchen sink at it, they’ll need to think again.”