The government's flagship plan to cap benefits at £500 a week per family has been thrown into crisis after the Liberal Democrats broke coalition ranks to complain that the policy risks increasing child poverty and homelessness.

In a move that suggests a more assertive approach by Nick Clegg's party, the Lib Dems have joined forces with leading charities and senior figures in local government to argue that a rigid cap could have a disastrous effect on families living in areas where the cost of housing is highest.

Jenny Willott, the Lib Dems' welfare spokesperson, told the Observer that she was pushing ministers to make major changes to avoid throwing more children into poverty and adding to homelessness. "I am very concerned about the effect on child poverty," she said. "There are a number of possible changes that are being discussed, but at the moment I am certainly not happy with what is being proposed."

Willott made clear she had Clegg's support and believed that ministers would amend their plans to ensure they pass through the Commons.

She wants ministers to build more flexibility into the system – and to consider removing child benefit from the cap altogether. This, she argues, would help families with children in areas such as London who could end up paying £400 a week on housing, leaving just £100 to meet their other costs.

The plan to impose a £500 cap was announced by the chancellor, George Osborne, at the Tory conference last autumn. But while the plans have proved popular with grassroots Conservatives, many charities and local government officials believe they are ill-conceived and rigid.

Roger Harding, head of policy at the housing charity Shelter, told the welfare bill committee in the Commons last week that the housing benefit cap undermined the underlying principles of the welfare state. "Analysis at Shelter shows that much of the south-east will become unaffordable to three-children families because of the cap. For a typical family of two adults – with one or both working – and three children, if both parents lose their job they will suddenly face not receiving enough housing benefit to live not only in their town, but in their region."

Government sources indicated that changes would be considered. "We can certainly look at transitional arrangements. We are not going to introduce anything that will make people suffer," said a source, adding that reforms were designed to bring greater fairness and the cap would be lifted as soon as those on benefits found work, creating a real incentive to find employment.