DELEGATES at the Scottish Liberal Democrat conference delivered a humiliating snub to their leadership yesterday, voting overwhelmingly against the Coalition's bedroom tax.

In an emergency debate, activists urged the Government to postpone the housing-benefit cut, due to take effect on April 1, to allow an independent investigation of its impact.

The vote – unanimous but for one delegate supporting the tax – was in spite of Scottish leader Willie Rennie and other LibDem ministers steadfastly defending it as a key part of cutting the nation's welfare bill.

As recently as Friday, Rennie said: "The bedroom tax is tough, but it is central to the welfare reforms."

The rift between the party leadership and members reflected the tensions in the Coalition on whether to change direction on the Tory-driven tax in Wednesday's Budget.

SNP Finance Secretary John Swinney last night urged the Chancellor to abandon the measure, warning in a letter to George Osborne that it would drain £112 million out of the economy over 30 years, as well as causing misery for thousands of families.

In calculating the financial drain caused by the policy, Swinney highlighted the tax's start-up costs as well as the increased cost of services for those affected, such as those forced into homelessness. This would combine with the economic impact of a large number of people left with less money to spend because of the changes.

Swinney said the Coalition's failed attempt to revive the economy through austerity was hitting the most vulnerable in society through "disastrous" welfare reforms. He said: "This policy is unfair, is unlikely to deliver savings in real terms, and cuts across devolved policies. I therefore urge you to withdraw it."

His letter coincided with Scottish councils highlighting the human cost of the bedroom tax being recorded by housing officers.

Examples gathered by the council umbrella body Cosla include a mentally ill man left in the home where his parents died being ordered to find an extra £16 a week from his £71 benefit; a blind man scared about being forced out of the house he has lived in for 30 years; and a widow being made to leave the home she has had for 50 years.

The bedroom tax is expected to affect around 105,000 working-age tenants in Scotland who rely on housing benefit for social housing.

Fourth-fifths of the households affected include an adult with a recognised disability.

Around 83,000 homes are deemed to have one "spare" bedroom, and so will lose 14% of housing benefit, while 22,000 with two or more spare bedrooms will lose 25%, leading to average extra costs of between £50 and £90 a month.

Leading the criticism of the tax, former LibDem minister Robert Brown, now a South Lanarkshire councillor, said it would cut people's "survival income". He said: "I hope that conference will send the clearest of messages to the Government, to Liberal Democrat ministers, that the policy is damaging and unfair."

Former MSP Mike Rumbles said he knew government involved compromises, but the bedroom tax was "mean-spirited" and "a nonsense".

There was also criticism of three MPs in the room – Alan Reid from Argyll & Bute, Malcolm Bruce from Gordon, and Mike Crockart of Edinburgh West – for failing to speak.

Edinburgh councillor Paul Edie said: "We haven't had a single Member of Parliament come up to this podium to defend these proposals. Why is that the case? I wonder if it's because it is indefensible?"

Delegates had earlier been harangued by a picket for working with the Tories to bring in the cuts, with protesters chanting "Shame on you for turning blue."

The vote on the tax came immediately before Rennie gave his keynote speech. In it, he said the LibDems were taking hard decisions for "the greater good" of society, but conspicuously failed to mention the bedroom tax or other welfare reforms.

"On aid, on the climate, on the economy, on fair tax it is the Liberal Democrats that are making the difference," he said.

Labour and the SNP called on Rennie and the LibDems in the Cabinet to listen to the party's grass roots and halt the bedroom tax.

Scottish Labour's Margaret Curran MP said: "Not a single delegate spoke in favour of the bedroom tax at the Scottish Liberal Democrat conference, but the Scottish LibDems around the Cabinet table – Michael Moore and Danny Alexander – want to support the Tories and carry on with a policy that will punish some of the most vulnerable people in our communities.

"100,000 tenants in Scotland will be hit by the bedroom tax, 40,000 face rent arrears and thousands could be made homeless."

SNP MP Dr Eilidh Whiteford said the LibDem conference had "descended into farce". She said: "It is now time for Scottish LibDems to reflect that it is their party which is complicit in imposing the bedroom tax. Voting against it in a small party event in Dundee may salve their consciences, but unless they take action to reverse the policy it will do nothing else."