Almost half a million UK families are thought to have fallen behind on rent, as a result of the coronavirus crisis, according to the Resolution Foundation.
It said more than 750,000 had been behind on housing costs last month.
That is 450,000 more than January 2020.
"Despite widespread calls for forbearance in the face of the Covid-19 shock, just 3% of private renting families have been able to negotiate a lower rent over the last 10 months," the think tank said in a report.
Meanwhile, one in 20 private renters in the UK said they had been refused rent reductions.
Many had taken "huge hits" to their earnings and had "limited savings" to fall back on, research director Lindsay Judge said.
"To make matters worse, measures that could ease the pressure, such as discretionary housing payments from local authorities and negotiated rent reductions from landlords, are not getting through to those that need them."
Almost one in four private renters had seen their income fall as a result of the crisis, the body said.
And it did not expect an easing of lockdown restrictions to be enough to solve their problems.
"Both benefit cuts and the end of furlough are pencilled in for the spring, either of which will strain family incomes further," it said.
"Likewise, unemployment looks set to rise, rather than fall, through 2021, potentially driving up arrears further still."
Landlords in England have been banned from evicting tenants until at least the end of March, offering "some security", the Resolution Foundation said, by preventing families under the most strain becoming homeless during the pandemic.
In Northern Ireland, landlords are required to give tenants 12 weeks' notice to quit, before moving to eviction proceedings. The rules were extended to March in anticipation of the second wave of the coronavirus pandemic.
But the Resolution Foundation also wants the government to offer loans to tenants to ease a "rent-arrears crisis" it expects to worsen in the months ahead.
Meera Chindooroy, from the National Residential Landlords Association, said loans would help tackle the rent debts owed to property owners.
"Simply banning repossessions is doing nothing to address this underlying problem which renters and landlords are struggling to cope with," she said.
A government spokeswoman said: "Robust protections put in place by the government remain - with the vast majority of renters still subject to six months' notice periods, while the ban on bailiff evictions in all but the most serious circumstances will stay in place until at least 31 March."