The average monthly rent for newly let properties has fallen for the first time since late 2010, says the estate agency Countrywide.
The drop has been due to a big recent increase in the supply of properties becoming available, mainly in London.
That was due to some landlords rushing to buy last year before a 3% stamp duty surcharge came into effect.
The average new tenancy in England, Wales and Scotland fell 0.6% in the year to February, to £921 a month.
The main factor was a big drop in rents in London and south east of England.
In the capital they fell by nearly 5% in the past year to an average of £1,246 a month, and in the south east of England they fell by nearly 3% to £1,152.
Everywhere else rental levels continued to rise.
"Rents are growing in most of the country but falls in London and the south east are dragging down the national growth rate, " said Countrywide's research director Johnny Morris.
"Early signs point towards 2017 being a rare year where rents rise faster in the north of the country than in the south," he added.
Countrywide's research is at odds with the most recent figures from the Office for National Statistics (ONS).
Its latest figures, for the year to January 2017, showed that across the UK rents for private tenants had risen by 2.2.%.
When the figures were published last month, the ONS commented that "inflation in the rental market is likely to have been caused by demand in the market outpacing supply" - a distinctly different message from that of Countrywide.
Countrywide said it expected the apparent over-supply of rental properties to be flushed out of the market in the coming year, with average national rents starting to grow again after that.