The average stock of homes per surveyor fell to a record low since data series began in 1978.
According to the latest Royal Institute of Chartered Surveyors (RICS) June Residential Market Survey, demand edged upwards for the second successive month.
RICS suggests the increase in house price growth is due to the acceleration in inflation experienced by the market during the second half of the year, as seen in the previous RICS UK Residential Market Survey.
The organisation said: "One reason for the slight recovery in buyer enquiries is likely to have been a further drop in mortgage rates which is accompanying the ongoing strength of the labour market."
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It is understood the West Midlands and London saw the strongest increase in potential buyers during the month.
41% more surveyors expect house prices to rise over the next three months, which is the highest proportion since April 2014 and 36% more surveyors expect sales to increase despite the flat trend in newly agreed sales.
RICS continued: "Across the rental sector, the demand and supply imbalance is also visible and landlord instructions, which have been broadly unchanged for the past couple of years and show no signs of a material increase, are at growing odds with the rising demand that is putting further upward pressure on rents."
Jeremy Blackburn, RICS Head of UK Policy said: "The Conservative Government has its sights set on a long-term project to drive owner occupation and property owning. This is of course at the centre of our society and economy.
"Our market survey shows, however, that it is not just in this area where there is a marked shortfall in supply. Just as significant is the pressure that is clearly building across the rental sector.
"Currently 36%, approximately 8.3 million households, are in rented accommodation. Rental is particularly important for enabling the younger more mobile workforce that it is central to improving our economic productivity."
(LM/MH)
