Jeremy Corbyn turned his fire on the Conservative cuts to local authorities during prime minister’s questions on Wednesday, suggesting the prime minister’s legacy would be rising poverty and crime.

The Labour leader avoided discussion of Brexit for the second week in a row as the two parties remain in talks over a possible compromise deal.

Instead he used the exchange with Theresa May to highlight child poverty in Swindon and Stoke-on-Trent, two authorities targeted by Labour before the local elections next month.

He said the prime minister’s legacy, a nod to her expected imminent departure, would be austerity and rising crime, rather than the help for struggling families that she had described in her first leadership speech.

“Child poverty is up, violent crime is up, homelessness is up,” he said. “This government stands for tax cuts for the richest and swingeing cuts for the rest.

“Will the prime minister now admit that far from tackling the burning injustices she talked about, her government’s cruel and unfair policies have pushed councils to the brink and left the just-about-managing not being able to manage at all? That is her legacy.”

Opening his questions, Corbyn mentioned the continuing talks between cabinet ministers and senior Labour figures, expected to continue on Thursday.

“As we continue discussions to find a compromise … we shouldn’t forget communities across this country that have been abandoned by this government in the here and now,” he said.

The Labour leader highlighted council cuts, child poverty and homelessness in both Swindon and Stoke-on-Trent, two councils which Labour hopes to target in the elections on 2 May.

Swindon, a marginal Conservative council, has a third of its seats up for grabs and Stoke-on-Trent, which has no overall control, is run by a Conservative and independent coalition.

“Take Swindon for example, where Honda recently announced 3,500 job cuts,” Corbyn said, highlighting statistics which suggest child poverty is more than one-third higher in Swindon than in Surrey, but the former has faced more than £235 per household in funding cuts.

“Why does Swindon face cuts when Surrey gets more money?” he said.

Corbyn also highlighted statistics on homelessness, three times higher in Swindon than Surrey, and food bank use in Stoke-on-Trent, where he said more than 4,000 parcels had been handed to children.

The prime minister said that councils had been asked to take “some difficult decisions, with regards to living within our means”, saying that had been down to the economic crisis under the last Labour government.

Corbyn said austerity in local government had been “a political choice” to impose the worst cuts on the poorest. “The evidence is clear, the Tories have abandoned communities across the country. They have left towns and cities to fend for themselves after nine years of vindictive austerity,” he said.