Rental prices continued to rise throughout the month as demand increased, but instructions from landlords fell, according to the report from the Royal Institution of Chartered Surveyors.
Overall, 45 per cent of property professionals reported buyer inquiries falling rather than rising, down from 20 per cent in May.
A net balance of 34 per cent of professionals also reported newly agreed-to sales falling rather than rising, which was weaker than the 8 per cent in May.
This was the most downbeat sales figure since December 2022, when a net balance of 38 per cent of professionals saw sales falling.
A net balance of 46 per cent of professionals reported house prices falling rather than rising, further deteriorating from 30 per cent in May.
The institution said some survey participants indicated that homes with better energy efficiency credentials were holding their value in the current market.
In the rental market, a net balance of 40 per cent of professionals saw an increase in tenant demand.
At the same time, 36 per cent saw landlord instructions falling.
With rising demand still being met with a lack of available properties to let, a net balance of 53 per cent of professionals expect rental prices to increase over the near term.
Figures from moneyfactscompare.co.uk on Wednesday showed that, across all deposit sizes, the average two-year fixed homeowner mortgage was 6.7 per cent, while the average five-year fix on the market was 6.2 per cent.
This week, average two-year fixed mortgage rates passed levels seen after last autumn’s mini budget.
“The latest increase in interest rates and the impact this has already had on mortgage rates is clearly visible in the key Rics metrics regarding buyer inquiries, sales and prices, which have all retreated over the past month," said Simon Rubinsohn, the institution's chief economist.
“Inevitably in this environment, activity levels are likely to remain relatively subdued.
"However, an important message coming back from Rics agents is around ensuring prices are set with an eye on the market conditions of today, rather than the recent past. When this is done, sales are taking place.
“It is also worth bearing in mind that house prices are only very modestly down on their recent highs and well above where they stood prior to the onset of the pandemic.
“Further declines are possible but need to be seen in the context of the previous strength in the market.
“Additional questions included in the latest survey also provide some support for the notion that, on balance, properties with better energy efficiency credentials are holding their value better than some others.”