This is a drop from an annual rate of inflation of 1.7% in December.
The average rent for a new tenancy starting in January was £888 per month, compared to £882 in January 2016.
Seven months of falls
UK rental price inflation has now fallen for seven months in a row, said Homelet, from a high point in June 2016, when rents were increasing at an annual rate of 4.7%.
The landlord insurance provider suggests that, if the current growth trend continues, average UK rents could start to fall within months.
The slowdown in rental price inflation has been most marked in areas that previously saw the largest increases. In Greater London, annual rental price inflation was just 0.4% in January, compared to a peak of 7.1% last July.
In the South East, annual rental price inflation is already negative, with rents on new tenancies agreed in January down by 0.6% compared to January 2016. As recently as last June, rents in the region were rising at a rate of 4.0%.
Martin Totty, HomeLet’s chief executive officer, said: “Our data has been showing, for some time, that landlords do not feel able to raise rents on new tenancies at anything like the pace seen during 2015 and the first half of 2016. Now it is even possible that rents will begin falling, which would be unprecedented in recent times.”