House price growth slowed to a three-year low in July 2016 as the vote for Brexit in the previous month's EU referendum weighed on the market, according to a leading survey. But the ongoing undersupply of homes and cheap mortgage credit should help underpin prices.

The Royal Institution of Chartered Surveyors (Rics) said just 5% more of its members polled reported higher prices than lower in July, down from 15% in June and the lowest reading since 2013.

New buyer enquiries and sales fell markedly, said Rics. A net balance of 34% more property professionals reported a fall in sales, the fastest decline since 2008. But over the long-term, there is less pessimism.

More of those surveyed expect sales to fall than rise over the coming 12 months with a -2% net balance. But this is a significant improvement on the -26% recorded in June. It was the third month of a negative reading on this measure, the worst streak since 2012.

"The housing market is currently balancing a raft of somewhat mixed economic news alongside the latest policy measures announced by the Bank of England, which have already begun to lower cost of mortgage finance," said Simon Rubinsohn, chief economist at Rics.

"Against this backdrop, it is not altogether surprising that near-term activity measures remain relatively flat. However the rebound in the key twelve month indicators in the July survey suggest that confidence remains more resilient than might have been anticipated.

"Critically, it is hard to escape the stark message regarding supply that is evident in the latest set of results with Rics data showing inventories on agents books around historic lows on average. This is a long running story that may have been exacerbated by recent events but clearly needs urgent action from the new government."

There are concerns the vote for Brexit on 23 June will plunge the economy into recession as investment decisions are delayed or dropped amid the uncertainty about the country's future relationship with the EU, in particular the single market. In response to the risk, the Bank of England slashed interest rates and boosted its stimulus package for the economy.