A 0.5% month-on-month uplift in August took the average price across the UK to £247,000, meaning the index surpassed a previous peak recorded in January 2008.
Overall, prices were 3.8% higher year on year, with England recording the strongest annual growth at 4.1%, but Scotland saw prices fall by 0.7% over the year typically. There were rises of 1.1% in Northern Ireland and 1.0% in Wales.
The housing market is expected to see the heat of demand from would-be buyers turned up further over the coming months, following the launch of the Government's new Help to Buy scheme, which offers state-backed mortgages to people with deposits as low as 5%.
Royal Bank of Scotland (RBS), NatWest, Halifax and Bank of Scotland started offering loans under the initiative last week and have reported strong interest so far, while more lenders including HSBC, Barclays and Santander have also confirmed their plans to come on board.
Some sharp increases in property prices in recent months have fuelled fears that the country could be heading for a property "bubble", with the new phase of Help to Buy pushing up demand for homes at a time when the number of properties for sale is in relatively short supply.
The ONS figures showed that first-time buyers are typically paying £185,000 for a property, which is 4.9% more than they would have done a year ago, while home-movers are paying £283,000 on average, marking a 3.3% annual increase.
Campbell Robb, chief executive of Shelter, warned that the Government's efforts to kick-start the market could actually result in properties being pushed further out of some people's reach as house prices increase.
He said: "Our rollercoaster housing market may make headlines, but these days rising house prices don't have the feel-good factor, and for good reason. Nobody wants a return to the bad old days of house prices rising then crashing.
"Unless house prices are stabilised, the grim reality is that - apart from a lucky few able to rely on the bank of mum and dad - soaring prices may well lead to the prospect of home ownership slipping even further away from even more of us."
Every region across England saw house prices rise year-on-year in August, with the strongest growth recorded in London at 8.7%.
House prices in England are now 1.3% higher than their previous 2008 peak, although in Scotland and Wales, prices are still around 5% below their peaks and in Northern Ireland they are 50% below their previous high.
Howard Archer, chief European and UK economist for IHS Global Insight, said: "While the strength of house price rises in London is becoming an increasing concern and pushing up the overall national increase in house prices, we are currently a long way off from an overall housing market bubble emerging.
"Indeed, in many areas house prices are still well below their 2007 peak levels and rising only modestly at the moment."
But he cautioned: "Nevertheless, there is a mounting danger that house prices could really take off over the coming months, especially if already significantly improving housing market activity and rising buyer interest is lifted appreciably further by the Help to Buy mortgage guarantee scheme."
A Treasury spokesman said: "We're encouraged to see signs that house prices are recovering from a low base alongside the wider economy.
"However, the Government understands that the housing and mortgage markets are yet to return to their long run levels, leaving too many people - especially first-time buyers - struggling to afford historically high level of deposits.
"That's why the Help to Buy mortgage guarantee is a vital tool to give young people the same opportunity to get a foot on the property ladder as previous generations."