The government's flagship plan to impose a £500-a-week cap on benefits paid to families has been denounced as immoral and deeply socially divisive in a savage attack by the former coalition minister for children and families.

In an outspoken interview with the Observer, the Liberal Democrat MP Sarah Teather, who was sacked from the government in September, says the policy will have devastating effects on many thousands of children whose lives will be disrupted as their parents are forced to uproot from their homes.

Teather predicts that there will be a "reverse Jarrow march" in the runup to next April, when the cap comes into force, as families head out of London in huge numbers, in search of new homes.

Accusing ministers of a deliberate attempt to denigrate those who cannot find work, Teather says she saw clear evidence while in government that the policy would not save money and that it would inflict immense social damage.

While accepting that the wider aim of encouraging people off benefits and into work is the right way forward, she says that imposing a cap on people who live in areas such as her own Brent Central constituency in north London, where rents are high, will have a "horrible" and "traumatic" impact. She also claims that the primary motive behind the policy, which has strong public support, was a desire to court popularity by unfairly demonising the poor.

"There are all sorts of things you have to do when times are tight that have negative consequences but you do them for good purposes. But to do something for negative purposes that also has negative consequences – that is immoral," says Teather. She praised Nick Clegg for showing "immense courage" in limiting some of the effects of welfare cuts and urged her party to fight as hard as it possibly could to prevent more. She said many people in her constituency, which is one of the most ethnically diverse and deprived in the country, did not realise what was about to hit them next April.

Middle-class families were also ignorant of the huge impact of the changes on those around them, particularly on children, because of the caricatures peddled by government and the rightwing press about those on benefits. She believes the effects may only sink in when children from "nice middle-class families who send their kids to the local primary school come home and say 'my friend has just disappeared'. I think then it might hit home and they might realise a whole set of children have disappeared from the class." Teather added: "I am frankly terrified about what is going to happen. A lot of these families do not know what is going to happen to them … How good is the education system at working out where that child has moved to? How good is the child protection system going to be at working out where children have moved to? I don't feel confident of that."

The £500-a-week cap is being imposed as part of government efforts to encourage people off benefits and into work in order to reduce the welfare bill. George Osborne, the chancellor, had indicated that £10bn more will need to be found in welfare savings in addition to the cuts already made as he tries to slash the deficit.

A spokesman for Iain Duncan Smith, the work and pensions minister, said: "The criticisms Sarah Teather is levelling against the government's welfare reforms are hugely misinformed and therefore result in needless scaremongering. It's not fair or right that benefits claimants receive higher incomes than hard-working families who are striving to get on in life. Our reforms bring fairness back to the system while ensuring we support the most vulnerable."

Last year the Observer revealed that the private secretary to Eric Pickles, the communities secretary, had written to the prime minister to warn that his welfare policies would increase the burden on taxpayers because families would be unable to pay their rent and would have to seek local government help in finding emergency accommodation.