May was the fifth month in a row which saw a decline in housing supply, while UK house prices reached record levels, climbing to £186,512.
In London, where the market is feared to be overheating, demand for new homes fell for the first time since June 2012.
Price expectations from surveyors dropped from 3.9% to 3.6% for the next 12 months
Simon Rubinsohn, RICS chief economist, said: “What we are really seeing is some of the very strong upward momentum starting to come off the housing market, as a lack of supply, higher prices, more prudent lending measures and some of the talk from the Bank of England are creating a level of caution among sellers and buyers.
“The most visible indicators of this are the revised downwards price expectations for the next 12 months and the flatter picture regarding new buyer enquiries. In particular, we’re seeing the London market level off.
“There is some evidence to suggest that the Mortgage Market Review has contributed to a tightening of the funding market, although it is hard to disentangle this from other factors which are now impacting on the sector and to know whether it will simply be a temporary influence as lenders adjust to the new environment.”
Just 29% of surveyors in the South East expect greater market activity in the next three months compared to 66% six months ago.
In the South West meanwhile the figure stands at 48%, down from 93% six months ago.
The tightening up of lending has led to a pick-up in demand in the rental sector, as rent prices are now projected to grow by 2.5% over the next 12 months and at an average annual rate of 4% over the next five years.
