Ministers came under new fire over benefit cuts last night as the independent body representing 1,200 English housing associations described the controversial bedroom tax as bad policy and bad economics that risks pushing up the £23bn annual housing benefit bill.

David Orr, chief executive of the National Housing Federation, said the tax would harm the lives of hundreds of thousands of people. It comes into force this week alongside a range of other tax and benefit changes.

"The bedroom tax is one of these once-in-a-generation decisions that is wrong in every respect," he said. "It's bad policy, it's bad economics, it's bad for hundreds of thousands of ordinary people whose lives will be made difficult for no benefit – and I think it's about to become profoundly bad politics."

His intervention came as opponents launched nationwide protests against the tax, which will hit 660,000 households with each losing an estimated average of £14 a week.

Crowds gathered in London's Trafalgar Square yesterday to protest against the measure, and simultaneous protests were being held in towns and cities across the UK. One protester, Sue Carter, 58, from Waltham Forest, told the Observer: "I'm a working single parent with a tiny boxroom and now I'm faced with the choice between food, heat or paying the bedroom tax. People have looked after their homes, improved them – why should they be turfed out?"

Under the scheme, which is introduced tomorrow, people in social housing with one spare bedroom will have their housing benefit cut by 14%, while those with two or more unoccupied rooms will see it slashed by 25%.

Ministers say the tax, which David Cameron calls the "spare room subsidy", will encourage people to move to smaller properties and save around £480m a year from the spiralling housing benefit bill. But critics such as the National Housing Federation (NHF) argue that as well as causing social disruption, the move risks increasing costs to taxpayers because a shortage of smaller social housing properties may force many people to downsize into the more expensive private rented sector.

The federation's warnings came as charities said the combination of benefit cuts and tax rises coming in from this week will amount to a £2.3bn hit on family finances.

Labour said analysis of official figures showed average families would be £891 worse off in the new tax year as the changes – including those to tax credits and housing benefits – begin to bite.

Research by the NHF says that while there are currently 180,000 households that are "underoccupying two-bedroom homes", there are far fewer smaller properties in the social housing sector available to move into. Last year only 85,000 one-bedroom homes became available. The federation has calculated that if all those available places were taken up by people moving as a result of the "bedroom tax", the remaining 95,000 households would be faced with the choice of staying put and taking a cut in income, or renting a home in the private sector.

If all 95,000 moved into the private sector, it says the cost of housing benefit would increase by £143m, and by millions more if others among the remaining 480,000 affected chose to rent privately.

As well as the move on spare bedrooms, council tax benefit will be replaced from this week by a new system that will be run by English local authorities but on 10% less funding. Pensioners will be protected under the changes but, as a result, it is feared there will be a bigger burden on poor working-age adults. Restrictions on the uprating of a number of welfare payments will also hit millions of households, homelessness charity Crisis has warned.

Chief executive Leslie Morphy said: "Our poorest households face a bleak April as they struggle to budget for all these cuts coming at once. People are already cutting back on the essentials of food and heating but there is only so much they can do.

"The result will be misery – cold rooms, longer queues at food banks, broken families, missed rent payments and yet more people facing homelessness – devastating for those directly affected, but bad for us all."

A Department for Work and Pensions spokesman said: "Our welfare reforms will improve the lives of some of the poorest families in our communities, with universal credit simplifying the complex myriad of benefits and making three million people better off. And by next year, we will have taken two million of the lowest earners out of paying tax altogether."

Crisis argues that homelessness is set to rise dramatically. This winter has already seen a rise of 31% in the numbers of rough sleepers across the country and a 20% rise in people seeking help with homelessness from their local authority in the past two years, according to Crisis.

ChartiesCharities are also concerned that the government-funded network of homelessness advisers in England is to be scrapped. The team of regional advisers and rough sleeper and youth specialists which have provided councils with expert guidance on meeting statutory homelessness duties since 2007 will be disbanded just as the bedroom tax comes in. Also being scrapped are the crisis loans and community care grants which provided a lifeline for people in financial crisis who needed essentials when moving to a new home.

Shadow chancellor Ed Balls said: "This is the week when the whole country will see whose side David Cameron and George Osborne are really on and who is paying the price for their economic failure."