'It now seems certain that we will have continuing political uncertainty, which the housing market traditionally dislikes, and with the first fall in June prices for eight years there is no doubt that the lack of stability is a factor, ' said Miles Shipside, Rightmove director and housing market analyst.
The average price in June was £301,114, down 0.2% on May.
Supply of new homes on the market continued to be restricted, though 7.6% more sellers coming to market this month compared to this time previous year, though June 2016 saw the Brexit vote hold the market back.
United Kingdom house prices are "virtually at a standstill" as consumers contend with a squeeze on living standards, Rightmove Plc said. "Buyers, many of whom are sellers too, will struggle to afford to pay much more".
That's up on the average of 0.1% for Wales and England.
The past month has seen a turnaround in expectations for interest rates, with three members of the Bank of England's monetary policy committee voting to raise the base rate from 0.25 per cent at the last meeting.
Despite this, prices are still up by 3.8% or £11,037 up on this time past year, however the Index shows that a North-South divide seems to have re-emerged. "High demand will continue to underpin prices, but we are seeing stretched affordability limiting the pace of rises, especially in the south of the country".
The number of sales agreed was up by 4.6 per cent in June 2017 compared to June 2016, and the number of sellers coming to market is also up on the same period a year ago, with a 7.6 per cent increase in fresh choice for buyers.
Jeremy Duncombe, director, Legal & General Mortgage Club, said: "Today's figures mirror the slowing of house price growth that we saw in the recent RICS survey, but activity in the mortgage market remains strong - and the property market outside of London and the South East continues to show healthy growth". On an annual basis asking prices for this sector of the market are 3.8% ahead of where they were in July 2016. We're also seeing a return to the North-South divide in terms of price growth.
The portal, in its latest monthly index, says the shortage of stock means that "prospective buyers in many parts of the country are seeing a lot of sold boards on properties they would like to buy themselves".
In a separate report on Monday, Deloitte LLP's Consumer Tracker showed confidence dropped the most in more than two years in the second quarter.