Surveyors say they are seeing evidence that the housing market is starting to cool.
In its monthly survey, the Royal Institution of Chartered Surveyors (RICS) found that 27% of professionals reported a fall in interest from potential house buyers.
It was the third consecutive month that interest from new buyers slipped.
Despite this, 65% of professionals said they had seen an increase in house prices, mostly due to a lack of available properties for sale.
This is lower than the high of 78% in April but still far above the long-term average of 13%.
Some 37% said they expected house prices to continue climbing in the next 12 months.
They found that average sales prices for properties listed at up to £500,000 were more likely to be above the asking price; in properties priced between £500,000 and £1m, 39% are seeing the sales price beat the asking price; and properties listed at over £1m are typically selling slightly below the asking price.
RICS chief economist, Simon Rubinsohn, said: "Although buyer inquiries have predictably slipped a little of late, this needs to be placed in the context of the healthy level of demand in previous months.
"A probably even more striking aspect of the latest report is the concern being voiced about the rental market."
Some 36% of professionals reported an increase in tenant demand, while 11% saw a fall in the number of new landlord instructions.
And 52% predicted that rents will rise over the coming three months.
The report also included comments from surveyors.
One, in Colchester, Essex, said: "Definite cooling off of the market, air of caution from buyers.
"Still demand for competitively priced properties and starting to see some reductions in values of those on the market in order to generate interest."
A Cornwall-based professional said: "Sales are still good, however it definitely feels like some of the heat has gone from the market."
One in Cardiff said: "Vendors, slow to accept changing conditions and rejecting early offers, are losing out. However, properties are still selling."
A surveyor based in Glasgow said: "The inevitable reaction to the squeeze on household budgets and rise in mortgage rates has arrived."
And one based in Belfast said: "The market has been very strong but I noticed it has slowed down slightly in the last month."