The government's benefits cap could make more than 80,000 children homeless and push many thousands more into poverty, says the Children's Society. In a devastating critique of the plan to limit the amount even the largest families can claim in benefits, Bob Reitemeier, its chief executive, said there would be a huge "human and social cost" if the reforms went ahead.

The welfare reform bill, which proposes a £500 a week cap on the amount families can claim for housing, childcare and sustenance, is set to return to parliament in the House of Lords on Tuesday after making unsteady progress through the Commons earlier this year.

The society says 200,000 children will have their lives affected by the changes to the amount their parents can claim and 27,600 adults and 82,400 children could be made homeless.

While supporters of the benefits cap claim it would simply mean families would be forced to move into cheaper accommodation, government figures suggest 70% of those who will be hit are already living in social housing.

Reitemeier said changes to the proposed legislation were urgently needed. "The reason we are so concerned about children is that three in four of the people that are going to be affected by the benefits cap are children and I don't think that's publicly understood", he said. "There are some main concerns: one is that the children will be made homeless, possibly 80,000 children, which would be a significant change to their lives.

"Secondly, what we think could happen is that those children already in poverty, below 60% of the median income line, will fall into severe poverty, less than 40% of the median income. This has a very human and social impact on their lives."

The Children's Society also believes that children, who are nine times as likely as adults to be hit by the cap because of the prevalence of large families among those claiming benefits, will experience lower levels of wellbeing. It says it understands the element of unfairness in people who are on benefits having large families catered for, but that the government should ensure children do not suffer for their parents' decisions.

The £500 cap is based on the average annual household wage of £26,000. The charity proposes that instead the government should work out the level of the cap – the universal credit – by basing it on the average household income of working families with children, which would include in-work benefits.

"Ideally we would say reverse the cap, but if it is a political agenda going forward then our view would be that the government should use average income, including in-work benefits for working families with children, to calculate the cap," Reitemeier said. "That would change the cap from £500 [a week] to a higher amount."

It is understood the charity's concerns are shared at the highest levels of the coalition government, particularly among Liberal Democrats.

Last night Karen Buck MP, the shadow minister for welfare reform, said she could not understand why the government was moving ahead with its policy. She added: "The household benefit cap will punish children disproportionately and increase homelessness with all the human and economic costs that implies. Worse still, cuts in childcare reduce the capacity of families to make work pay and so avoid the cap.

"We saw from leaked warnings this summer that the housing department fears that Department for Work and Pensions cuts will increase homelessness and now this is being confirmed. What is the point of policies which cost more than they save?"

A spokeswoman for the DWP said that additional take up of benefits due to the simplicity of the new system would actually take nearly a million people out of poverty. She added: "Someone in work should be better off than someone on benefits - this is at the heart of our welfare reform. There must be a clear incentive to work. No one will be worse off as a result of Universal Credit."