New figures published by Edinburgh City Council showed the number of those with spare bedrooms who were unable to pay rose from 969 to 2,561 in the eight weeks following 1 April.
This meant that about 72 per cent of those affected by the changes did not pay, following cuts to their housing benefits.
Tenants with one spare bedroom lost 14 per cent of their payments, leaving them to make up the difference from April. Those with two spare bedrooms lost 25 per cent.
About 3,560 of the 20,000 council homes in the city are affected.
Council leaders said they hoped increases in funding for Discretionary Housing Payments – effectively crisis grants – would ease the burden temporarily, but said there was no long-term solution.
Ricky Henderson, the city’s health, social care and housing leader, said: “People who are unable to pay are incurring a substantial personal debt, which is going to stay with them until they pay it off.
“We have invested in advice services and we are offering Discretionary Housing Payments, but they are really only short-term and there is no permanent solution in sight.”
The bedroom tax was introduced by Westminster to encourage social housing tenants with a spare bedroom to downsize, but many local authorities, including Edinburgh, say that, even if tenants wished to do so, there are too few one-bedrooms in the first place.
Steve Burgess, Scottish Greens convener on the council, said the local authority had to do more to make tenants more aware that help is on offer.
He added that only 1,000 of the 2,500 tenants behind on payments had applied for the crisis payments.