Eight Scottish councils appear on a list of the 20 areas in the UK where rent arrears have mushroomed since the policy was introduced in April.
In Clackmannanshire, more than two in three of those affected, 67%, have fallen behind with their rent. In Dundee that figure was 49%, in Renfrewshire 47%, North Lanarkshire 46%, South Lanarkshire 45%, Edinburgh 45%, East Ayrshire 44% and East Renfrewshire 42%.
The figures were uncovered by the TUC-backed False Economy group, which warned the problem was likely only to get worse.
Under the policy, council or housing association tenants who are deemed to have an extra bedroom have their housing benefit cut by 14%. The group said that as a result many households were relying on emergency help from councils that would soon dry up.
Citizens Advice Scotland's chief executive Margaret Lynch said her organisation had seen a 40% increase in the number of people asking for advice on rent arrears since the under-occupancy charge was introduced,
Ms Lynch said: "It's a very worrying trend, and our advisers report that many of these people are turning to desperate measures, such as payday loans, or are having to use food banks because their budget is now so stretched.
"The Government is saying councils are not providing people with the support that will alleviate the problem. That may be true in some cases, but the real problem is the policy itself is deeply flawed. It is targeting the poorest people in society, and making them even poorer.
"People who live in homes with 'spare' rooms are not in that position by choice. It's the home they were allocated. And many families have adapted those homes over the years to cater for disabled relatives. They are now being told to move to smaller properties, which in many areas simply do not exist. Many of these people feel they are being punished for something over which they have no control."
Clifford Singer, from False Economy, said: "The worst part is these figures have been collated while councils' emergency Discretionary Housing Payments are still available. They are being used up at record speed. When they run out, the figures will only get worse."
Ministers say the reforms bring the rules for council houses into line with those for private accommodation and will free up homes for those who need them.
But campaigners accuse the UK Government of forcing families into poverty. They also warn the policy will cost the taxpayer more by pushing people into the private rented sector.
The Department for Work and Pensions dismissed the rent arrears figures and said the policy was a "necessary reform to return fairness to housing benefit".
A spokesman said: "It is wrong to suggest the early stages of the policy - as people start to adjust to the changes - represent long-term trends in any way whatsoever.
"We are carefully monitoring the policy nationally, ensuring the extra funds to support vulnerable tenants are used well as these changes are introduced."
"Even after the reform we pay more than 80% of most claimants' housing benefit - but the taxpayer can no longer afford to pay for people to live in properties larger than they need. It is right that people contribute to these costs, just as private renters do."
TUC general secretary Frances O'Grady said: "It says a lot about this Government's commitment to fairness that it has blocked a mansion tax for millionaires, but is happy to go ahead with a bedroom tax on disabled and low paid families."