Annual price growth also rose to 9.6% from 8.6% in May – the highest rate since September 2014.
The average UK house price has now risen by £200,280 after increasing by 1.7% month-on-month.
Jeremy Duncombe, director of Legal & General Mortgage Club, said: “With continued house price growth following the election, the market remains unaffordable for many.
“A projected surge in demand in the second half of the year will work to further exacerbate this issue by pushing house prices even higher.
“The best way to bring long-term stability to the housing market is to boost the supply of new homes in order to keep up with demand.
“We hope to see housebuilding at the heart of today’s budget, along with a concrete strategy on how the government plans to deliver on their promise to boost supply.”
Halifax’s housing economist Martin Ellis agreed that supply is very tight, causing further price growth.
House prices per square metre have risen by 18% from £1,719 in 2010 to £2,033 in 2015.
Ben Thompson, managing director of estateagent4me.co.uk, said: “In light of today’s figures, we would predict that house prices will continue to rise steadily as we move into the second half of the year.
“This increase will in part be driven by the ongoing imbalance between supply and demand of housing stock.
“In order to see a healthy market across the whole of the UK, as an industry we need to do more to tackle the current housing crisis.
“More suitable homes need to be built in key areas, helping to ensure prices don’t become unsustainable, keeping the market fluid, and enabling more people to achieve their goal of homeownership.”
