Rental price growth more than halved last year as the nation hit "an affordability ceiling".
UK rents increased by an average 1.7 per cent year-on-year in December, according to data from Homelet, down from rent inflation of 3.8 per cent last year.
New tenants paid an average rent of £892 per month.
Read more: Rents in London fell slightly in December
In London, the average rent increased two per cent from £1,478 per month in December 2015 to £1,508 per month last December.
This annual increase was down from a growth of 6.8 per cent in the middle of 2016, which, Homelet said, showed that rent rises were becoming unfeasible.
Martin Totty, HomeLet's chief executive, said: "While demand for rental property remains strong, landlords always have to be mindful of tenants' ability to pay higher prices.
"We have now begun to approach an affordability ceiling, particularly in areas of the country where rental price inflation was previously highest."
Some commentators in the property industry have said that government measures that increase landlords' costs - including chancellor Philip Hammond's decision to abolish letting agent fees for tenants - will push up rents.
However, Totty said that any move to increase rents could be "problematic" in parts of the country that are already expensive, as tenants simply won't be able to afford higher prices.
The news comes after data from Landbay showed that some tenants in London (those living in one bed properties) have to shell out almost three quarters of their disposable income on rent.
Homelet reported that, on average, a Londoner spent 31 per cent of their income on rent in December.
However, with such a shortage of affordable housing in the capital, many Londoners have no choice but to rent.
“The private rented sector is now having to cope with a series of disruptive elements, just at a time of great economic uncertainty, and amid a continuing systematic imbalance between supply and demand for residential property," Totty said. "The assumption that landlords have sufficient means to bear higher costs will soon be tested. Tenants must hope they do.”