Homebuyers are returning to the market as it settles after a turbulent few weeks following the vote for Brexit at the end of June.
The Royal Institution of Chartered Surveyors (Rics) said the level of new buyer enquiries rose for the first time in seven months during September.
In its UK Residential Market Survey for the month, a net balance of 8% more respondents reported higher than lower demand, up from -5% in August and a substantial recovery from June's -34%, though there are regional differences beneath the headline figures.
"The market does now appear to be settling down following the significant headwinds encountered through the spring and summer," said Simon Rubinsohn, chief economist at Rics.
"Buyers do appear to be returning, albeit relatively slowly, but the big issue that continues to be highlighted by respondents is the lack of fresh stock on the market. Although this is not a new story, it is a significant one having ramifications for both prices and the level of turnover."
That underlying shortage of stock is driving up prices. Rics said its net balance for prices hit +17% in September, with more agents reporting rises than falls, up from 13% in August.
Britain will formally begin negotiations to leave the EU when it triggers Article 50 of the Lisbon Treaty, which the government said it will do by the end of March 2017.