Latest data from the Office for National Statistics (ONS), which covers costs for all privately-renting tenants - including those who are not moving - shows rents rising at 8.7% a year.
Zoopla tracks rents when homes become vacant and are re-let at an open-market rent, accounting for about a quarter of the rental sector.
The property portal has forecast rents rising at an average rate of 4% next year, with demand still outstripping supply.
The increase would come, in part, as a result of fewer properties being made available by landlords.
The National Residential Landlords Association (NRLA) said that 31% of landlords were planning to sell properties they rent out in the next two years.
It wants changes to housing taxation and reassurances over no-fault eviction rules.
"What tenants need is greater choice. That means encouraging and supporting the vast majority of responsible landlords to stay and continue to provide decent quality housing," said Ben Beadle, chief executive of the NRLA.
Ben Twomey, chief executive of Generation Rent, which lobbies on behalf of renters, said that more breathing space should be given to tenants facing cost-of-living pressures.
"The government must act urgently to slam the brakes on rising rents, whilst unfreezing the Local Housing Allowance rate will protect families on low incomes from poverty and homelessness," he said.