Buyer demand rose for the first time in seven months in September, the Royal Institution of Chartered Surveyors (Rics) said.
It had dived in June and July during the height of the referendum battle and immediate aftermath of the Brexit vote.
The lack of properties coming onto the market means that prices have risen.
Members of Rics said that the average of 45 properties on estate agents books remained close to historic lows.
“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.”
Over the next three months, surveyors predict that house prices will rise further on a national basis.
However, there remained a greater level of caution in central London where prices were expected to fall, albeit only modestly, over the same period, Rics said.
Recent surveys by mortgage lenders, the Halifax and Nationwide, suggested that annual increase in house prices had slowed in September compared with the previous month.