Bishops across the country, backed by Rowan Williams, the archbishop of Canterbury, have condemned the coalition government's controversial welfare reforms, which they say risk pushing thousands of children into poverty and homelessness.

Eighteen Church of England bishops, backed by Williams and the archbishop of York, John Sentamu, are demanding that ministers rewrite their flagship plan to impose a £500-a-week benefit cap on families.

In an open letter in Observer, they say the Church of England has a "moral obligation to speak up for those who have no voice". Their message is that the cap could be "profoundly unjust" to the poorest children in society, especially those in larger families and those living in expensive major cities.

The high-profile intervention comes after the Church of England became embroiled in an embarrassing row over its attitude to anti-capitalist protests outside St Paul's Cathedral in London. One cleric resigned over plans to evict the protesters forcibly, arguing that the Church should have been more supportive of their cause.

The bishops are calling on ministers to back a series of amendments to the welfare reform bill – due to be debated in the House of Lords tomorrow – that have been tabled by the bishop of Leeds and Ripon, John Packer.

A spokesman at Lambeth Palace said Williams was fully behind the bishops' initiative. "As a president of the Children's Society the archbishop fully supports the proposed amendments to the welfare reform bill."

Sentamu also threw his weight behind the changes. "I hope that the government will listen to the concerns being raised and ensure that children, especially the most vulnerable, are protected from cuts to family benefits."

Under the bill, which is facing huge opposition in the Lords, the government plans to limit the amount any household can claim in benefits to £500 a week, to ensure state handouts cannot exceed average weekly wages for working households.

Ministers, who announced the cap at last year's Tory conference, say the reforms will encourage people back to work while cutting the £192bn a year spent on welfare payments. But the Children's Society claims the policy will cut support to around 210,000 children and make as many as 80,000 homeless.

Packer has tabled five amendments to the bill, drawn up with the help of the society. The suggestions include: removing child benefit from household income for the purposes of calculating the level of the cap; calculating the level of the cap based on earnings of families with children, rather than all households; removing certain vulnerable groups from the cap; and the introduction of a significant grace period of exemption from the cap for households in which people have recently left employment.

The bishops call on the government to act to prevent plunging "some of the most vulnerable children in the country into severe poverty". They add: "We do hope the government will listen to, and act upon, our plea, for the sake of some of the most vulnerable in our society."

Speaking to the Observer, Packer said he understood the aim of the government to encourage people back into work. But he felt "absolutely clear" that the cap would cause "hardship and unintended consequences which we need to prevent". He said: "I think it is the care for children which is particularly important to me in this whole debate about welfare and about the way in which people are treated in our society."

It was also vital, he stressed, to take in the effect on people who cared for the children of others. "One of the things which has been raised is that some large families are actually created by the fact that people have taken on other people's children. That may be in circumstances where the parents have died or for some reason the parents can't look after them, and it is often relatives who have taken them in. This could be a real discouragement to people to take on caring responsibilities."

The bishops who have signed up to today's letter are from the dioceses of Bath & Wells, Blackburn, Bristol, Chichester, Derby, Exeter, Gloucester, Guildford, Leicester, Lichfield, London, Manchester, Norwich, Oxford, Ripon & Leeds, St Edmundsbury & Ipswich, Truro and Wakefield.

The bishop of Truro, Tim Thornton, said the unity of the bishops should convince the government to act. "We are proposing something positive rather than just saying something negative."

The Rev Leo Osborn, president of the Methodist Conference, added his support: "The benefit-capping policy will lead to a reduction in the living standards of the poorest in society. It risks creating perverse incentives for families to break up: under this proposal a family with four children could be better-off if it split into two single-parent households."

A Department for Work and Pensions spokesperson defended the policy. "It simply isn't fair that households on out-of-work benefits can receive a greater income from the state than the average working household gets in wages. This is why we have proposed a benefit cap of around £500 per week.

"Many working-age families with adults in work cannot afford to live in central London, for example, and it is not right for the tax payer to subsidise households on out of work benefits who do."

Many Liberal Democrat and crossbnench peers also oppose a rigid benefit cap and believe ministers will give ground.