Falling buyer confidence is holding back price growth, as just 16% of surveyors report prices rising down from 50% at the start of the year.
The survey also highlighted that London is the only part of the UK where all surveyors are seeing property prices fall instead of rise.
The survey showed that new buyer enquiries fell for the third consecutive month, slumping to their lowest level since the middle of 2008. The south of England showed the sharpest decrease in demand, with more than half (58%) of surveyors observing a decline. RICS said that anecdotal evidence suggested that EU referendum uncertainty was largely to blame for the slump.
The supply of properties also took a nosedive, according to the survey. The volume of properties available for sale dropped across the UK, except in Northern Ireland. Nearly half or 45% of survey contributors reported a decline rather than a rise in new instructions over the month: the steepest fall on record, according to the RICS.
More than a quarter of contributors also said they expected a decrease in sales activity over the next three months. Sales expectations for the year ahead turned negative for the first time in four years, with 12% more contributors expecting transactions to fall during this time frame.
Tenant demand increased slightly in June, with 12% more respondents seeing a rise in demand, but there was also a small drop in the number of new landlord instructions.