The government's safety net for those facing hardship as a result of swingeing housing benefit cuts, amounts to a "drop in the ocean" of a mere £1.30 a month per household in the first year, according to housing associations.

The study, published ahead of a parliamentary debate on the proposed changes to housing benefit, reveals that the government's own figures calculate that 642,000 households will lose £39 every month because of the reforms.

The National Housing Federation says such a "brutal cutback" will leave hundreds of thousands of low-income families facing the prospect of "falling into debt or hardship or being forced to move out of their home and away from their local community to live in cheaper accommodation further afield".

To counter the backlash from the reforms, ministers announced an extra £130m for local authorities' discretionary housing payment over the next four years, with £10m put up next year.

Even if the new cash was distributed equally among all the households affected by the cuts, the federation said it would equate to only 30p a week in the first year and £1.20 a week from 2013.

The federation's chief executive, David Orr, said: "The transition fund is a drop in the ocean when you consider that these brutal cutbacks will leave over 600,000 families significantly worse off and plunge many into severe debt, poverty and force some families out of their homes. In reality, this fund will only stretch to help 13% of households cover the full cost of the losses they will suffer once the cutbacks are introduced." An analysis shows that in big cities the shortfall faced by tenants would all but swallow up government payments offered to those in need. In Manchester the amount required for tenants would be more than £6m. In Edinburgh, the shortfall would be more than £5.5m next year. Even in sparsely populated Cornwall benefit claimants need £5m to cover their losses.

Ministers last week robustly defended the "substantial increase in the discretionary housing payments budget, which will allow local authorities to give additional support where it is most needed".

Labour warn, however, that the extra money is likely to be swallowed up by the 50,000 most vulnerable families placed in accommodation to prevent them becoming homeless each year. Karen Buck, Labour's welfare spokeswoman, said that "even if you apply the national average shortfall to the 50,000 families who are assisted in the private rental sector that leaves a funding difference of £10m. It is not enough money to cover the losses of the most vulnerable."

The dispute follows the publication of data by the Guardian that revealed the south of England could be emptied of affordable properties for those on benefits within 15 years. This data has also been used by Labour to back arguments that the government should rethink the policy. However, Iain Duncan Smith, secretary of state for work and pensions, said Labour had "behaved disgracefully" over housing benefit and "has been spreading panic and lies in a cynical attempt to disguise their own incompetence".

The cabinet minister produced new figures showing that without these changes the country would have been left with a £25bn housing benefit bill. "By 2015, every working household would be paying £1,515 a year for Labour's broken system. Does Ed Miliband think it is fair that working households should pay over £1,500 each to subsidise the housing benefit bill in five years time? And if not, what is his alternative plan to reform housing benefit?"

Meanwhile, Opposition spokesman on local government Lord Beecham today wrote to the chancellor, George Osborne, demanding an apology for misleading the public in his spending review statement, in which he claimed that £5bn was lost to fraud in the benefit system every year. Figures obtained by Beecham through a written parliamentary question to the welfare reform minister Lord Freud reveal that although £5bn is lost in the system each year, £3.5bn of that amount is lost through error and £1.5bn through fraud.

• This article was amended on 11 November 2010. The original referred to Lord Beecham as a former Labour minister. This has been corrected.

