Prospective buyers are "seeing a lot of sold boards on properties they would like to buy themselves" with over 45% of estate agents' property stock now being sold subject to contract.
In the East of England asking prices increased by just 0.6% month on month to £351,276 but are still 3.8% higher than a year ago and in Wales they increased by 0.8% to £184,308 but are 0.5% down year on year.
In annual terms, prices were up 2.8 % compared with a 1.8 % rise in June.
"It is likely that, should these figures ring true, we could see a reverse in the cooling price trends reported over the last month or so, but heightened seller activity must be matched on the buyers' side of the market in order for this to happen, otherwise, we could see the reverse".
'The price of property coming to the market had increased in June in every year since 2009, so buyer confidence has clearly been affected by inflation outstripping their pay packets and current political events, ' he pointed out.
Modest growth over the past 12 months sees average asking prices across England and Wales rise by 2.8 per cent to £316,421, which although is in line with market forecasts and expectations for this year, is far lower than the rises recorded a year ago.
House prices remain flat a year after Brexit - Rightmove
Murphy explained the United Kingdom property market is seeing the highest levels of stock sell-through since Rightmove started to track the metric - which is means demand for property remains strong with consumer confidence largely undaunted, and underlying market fundamentals remaining robust.
A jump in inflation to almost 3 percent has hurt the spending power of many people in Britain, contributing to a slowdown in the economy and in house price rises. Although for first-time buyers, the figure fell 1.7 per cent month-on-month, from £196,943 in June to £196,450 this month.
Compared to the period around the referendum a year ago, more sellers have come to market and more buyers are buying.
"Prices are in the summer doldrums", said Mr Shipside.
Rightmove director Miles Shipside said high demand would continue to support house prices in the coming months but that a squeeze on consumers' purchasing power would limit the rate of price rises.
"Other factors, such as the average time to sell standing at 60 days in this month's report, has remained broadly unchanged now for the last quarter, and also points to market consistency in most areas that again flies in the face of some who might suggest that the market is in negative territory".