The average value of a UK property was £223,257 in June 2017, according to the Office for National Statistics.
The annual growth rate has slowed since mid-2016 following the European Union referendum, from a high of 8.2 per cent in June last year at the time of the vote.
But it has remained broadly around 5 per cent during 2017.
House prices rose by 0.8 per cent on a monthly basis between May and June, an increase on the previous monthly rate of 0.5 per cent.
John Goodall, chief executive of Landbay, said: “Against expectations inflation has held steady today, stealing the limelight from housing figures, which suggest that house price growth has now returned.
“Supply and demand remain severely out of kilter, meaning that housing affordability remains one of the most pressing issues facing UK society over the medium to long term.
“The roots of the affordability crisis can be traced back to insufficient construction over the past decade, but a number of other macroeconomic factors are now also playing a part.
“Wage growth is struggling to keep pace with rocketing inflation, which is hitting people’s pockets and making it harder for aspiring homeowners to afford their first property, as well as discouraging existing homeowners from moving.”
The national figures disguise different levels of house price inflation in the decade since the financial crisis.
England is the only British nation to see its house prices rise significantly above the pre-recession peak of £195,000 in September 2007, with the average house price now at £238,000.
Meanwhile this month Wales became the only other nation to see its house prices surpass their pre-recession peak, with the average house now costing £152,000 compared to £150,000 in October 2007.
Scotland’s average house price is still £2,000 below its pre-recession peak at £144,000 while house prices in Northern Ireland are 40 per cent below their level in September 2007 at £129,000.
The local authority showing the largest annual growth in the year to June 2017 was the Orkney Islands, where prices increased by 27.9 per cent to stand at £148,000.
Meanwhile the lowest annual growth was recorded in City of London, where prices fell by 20.3 per cent to stand at £724,000.
London was the only region of England to see house prices decrease on a monthly basis, with the average price falling by 0.7 per cent to £481,556.