Labour must “get its act together” so it can defend low-paid workers who are facing the most concerted attack on their living standards in a generation, the head of the UK’s biggest public service union has said.

Dave Prentis, the general secretary of Unison, said it was unacceptable that while tens of thousands of teaching assistants, carers and support workers were worrying about how they were going to “put food on the table” because of the government’s austerity programme, members of the shadow cabinet were indulging in infighting.

“Right now, our members – many of them low-paid women – are lying awake at night, wondering whether they will have a job in a few months or fretting about how they are going to feed their children once the tax credit cuts hit,” he said. “Meanwhile, we have a Labour party which does not seem to be focused on standing up for them. Labour cannot afford to degenerate into infighting.”

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The warning follows a series of statements and briefings by the party’s MPs, which critics say have been intended to undermine the Labour leader, Jeremy Corbyn. In the latest case, Maria Eagle, speaking on BBC1’s Andrew Marr Show, backed the head of the armed forces when he voiced opposition to the Labour leader’s position on Trident nuclear weapons.

Prentis said voters would not forgive the party if it turned in on itself rather than defending the vulnerable and low-paid who were under “unprecedented attack” from the Tory government.

“People will not vote for a divided party so Labour has got to get its act together,” he said. “They have got to recognise that the real enemy is a Tory party devastating the lives of millions of low-paid families – not other people within the Labour party.”

It emerged on Thursday that Jeremy Corbyn is planning to protect himself from any challenge to his leadership by ensuring he remains on the ballot paper even if the parliamentary party declared they had lost faith in him.

It was reported last night Corbyn was planning to raise the issue at a meeting of the national executive next week, but in practice any rule change guaranteeing a sitting leader spurned by the parliamentary party remaining on the ballot paper could only be agreed by the party conference in the autumn.

One party rule in the section on the leadership states: “Where there is no vacancy, nominations may be sought by potential challengers each year prior to the annual session of party conference. In this case, nominations must be supported by 20% of the Commons members of the PLP.”

Arguably, this leaves Corbyn open to challenge annually before any autumn conference and the party leader would need the support of a fifth of Labour MPs to stand again.

In practice, Labour MPs, collectively largely opposed to Corbyn, sense that they cannot exclude him from the ballot paper if they passed a motion of no confidence in him and he still wanted to stand. If Corbyn stood down, the Left want to ensure that the filter of moderate Labour MPs cannot block leftwing candidates from standing.

Unison backed Corbyn in the Labour leadership election and Prentis, who is standing for re-election as general secretary, said the impact of the tax credit cuts combined with further attacks on public services were hitting women particularly hard – and driving millions of families close to destitution.

“We are now seeing that our members – who are often women in work with families – are being hit the hardest. For someone on £20,000, their take-home pay is being reduced by 10%. This is devastating and is affecting 2.7 million families, 5 million children.”

George Osborne is coming under growing pressure over his deficit reduction plans from within the Conservative party. The former Tory prime minister, Sir John Major , criticised the “shocking” impact of inequality in Britain, saying more was needed to be done to tackle the gap between rich and poor.

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And a Conservative-controlled select committee condemned Osborne’s proposed changes to tax credits on Wednesday, urging him to consider a pause to undertake a fundamental rethink of his priorities.

Prentis issued a direct appeal to the chancellor to think about the impact his “cruel” policies were having on millions of people across the country. “You have got to row back on the whole idea of taking money away from low-paid workers who have suffered so much since the recession,” he said.

“These are people who work, people who never expected to be hurt in this fashion. It is cruel and shows a complete lack of understanding of how much people have gone through over the last seven years.”

The chancellor is expected to announce further deep cuts to public services in the spending review later this month, with four departments already accepting cuts of 8%. Prentis warned there were real concerns that, as funds dried up, crucial, statutory public services would cease to exist.

“We are seeing a collapse in home care, the collapse of residential care … There are serious, serious concerns about about how public services are going to be able to carry out the functions that are required of them to keep our communities safe,” he said.