In the short-term, price expectations climbed into positive territory for the first time since April, with a net balance of 10 per cent of surveyors now anticipating a rise in prices over the coming three months.
Simon Rubinsohn, Rics chief economist, said: 'There are clear signs that the housing market is settling down after the initial surprise of the outcome to the EU referendum.
'Buyer enquiries did dip again in August but only modestly, and more significantly, sales expectations are beginning to edge upwards once again.'
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The report confirmed data from the Bank of England which showed mortgage approvals dropped sharply from 64,200 loans in June to 60,900 in July following the referendum vote, but added that the picture was now stabilising.
It also suggested that surveyors expect the number of home sales to rise in every region of the UK over the next 12 months and that, despite this, an ongoing shortage of property for sale would keep prices propped up.
This was already the case, said the report, with a net balance of 12 per cent of surveyors reporting house prices rising rather than falling in August, up from a balance of 5 per cent the previous month.
Recent economic news is taking a more positive tone and it looks increasingly likely that the housing market will avoid catastrophe.
For the sixth month in a row, more surveyors in London reported prices falling rather than rising but in most other parts of the UK, prices showed signs of increasing.
East Anglia and the West Midlands had the strongest price growth, with balances of 30 per cent and 22 per cent of surveyors respectively in these areas reporting prices rising rather than falling.
In Wales, a net balance of 13 per cent of surveyors reported prices rising rather than falling, and in Scotland and Northern Ireland the balance of surveyors reporting rising prices was 17 per cent.
Hansen Lu, of Capital Economics, was circumspect but admitted there are 'increasing signs that the initial post-referendum shock has begun to recede'.
He added: 'With buyer numbers still falling and confidence still shaky, the weakness in transactions will last for several months yet, while house price growth will continue to ease. But with the recent economic news taking a more positive tone, it looks increasingly likely that the housing market will avoid catastrophe.'
Surveyors expect the number of home sales to rise across the UK over the next 12 months