Ed Miliband has given a commitment that a future Labour government will abolish the "bedroom tax", in a move that is likely to be highly popular with the party's natural supporters.

The eve-of-conference pledge marks the start of the unveiling of a range of policies designed to ease the living standards crisis, including proposals to strengthen the minimum wage in specific sectors over time as the economy improves.

Miliband will describe the bedroom tax as "a symbol of an out-of-touch, uncaring government standing up for the interests of the privileged few, and never for you".

The Labour leader will claim that two-thirds of the 66,000 people affected are disabled, and say that the vast majority do not have the option of moving into smaller accommodation.

The bedroom tax pledge will cost as much as £470m, but Labour said the costs can be met by closing tax loopholes in the construction industry, abandoning the government's shares-for-rights scheme and reversing George Osborne's £150m tax cut for hedge funds announced in the budget in 2013.

The estimated savings in construction come from a clampdown on the so-called disguised workers scheme, a means whereby workers pretend to be self-employed to reduce tax.

It is the first time Labour has given an unambiguous pledge to repeal a government welfare reform and will put pressure on the Liberal Democrats in the Commons to support abolition after its own party conference also called for the scrapping of the bedroom tax.

The TUC last week found that one in three council tenants have fallen behind on their rent since the introduction of the bedroom tax; in some areas, including Barrow and Cumbria, the figure reached three-quarters of council tenants.

The bedroom tax, part of the 2012 Welfare Reform Act, was introduced in April and charges working-age tenants in social housing based on how many spare rooms they are deemed to have.

Benefits are reduced by 14% for one room and 25% for two or more bedrooms. On average, a tenant affected by the bedroom tax is losing between £14 and £25 a week.

Ministers – who prefer to refer to the policy as the removal of the "spare room subsidy" – have introduced discretionary payments for councils to ease the impacts on tenants.

A poll released on Friday by the National Housing Federation (NHF) shows almost three in five people (59%) think the government should abandon the policy entirely. Some 79% of the sample who intend to vote Labour in the next election believe the government should abandon the bedroom tax, while five in six (83%) potential Labour voters say the policy shows the government is out of touch.

Two-thirds (65%) of potential Liberal Democrat voters and more than a third (34%) of people who intend to vote Conservative in the next election say that David Cameron should abandon the bedroom tax entirely and think of other ways to save money.

The NHF also surveyed 51 housing associations and found that half of families hit by the bedroom tax were pushed into debt in the first three months of the policy.

Nick Clegg, the Liberal Democrat leader and deputy prime minister, has continued to defend the tax, saying that 250,000 families were living in overcrowded accommodation, yet 1 million tenants have spare bedrooms. He claimed the coalition was simply applying the same principle to the social rented sector as Labour applied to the private rented sector.

A Department for Work and Pensions spokesman said: "It is simply not affordable to pay housing benefit for people to have spare rooms. Even after our necessary reforms, we continue to pay over 80% of most claimants' rent if they are affected by the ending of the spare room subsidy.

"We are also giving local authorities £190m funding this year, so vulnerable claimants get the help they need during the welfare reforms."