The average monthly rent for newly-let properties has fallen for the first time since late 2010, according to 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 the 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."
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 rents for private tenants across the UK 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 different message from that of Countrywide.
Countrywide reported that across Britain there had been a 5% rise in the number of people looking for homes to rent during the past year, but in London, and the south east of England, the number of would-be tenants had dropped, down by 3% and 5% respectively.
Everywhere else, the estate agency said, tenant demand had continued to grow, especially in the East Midlands, the east of England and the north west of England.
On the other side of the coin, Countrywide said that in February this year there were 10% more homes available to rent than a year ago.
But the agency expects this 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.