A 0.5% month-on-month uplift took the average price across the UK to £247,000, meaning the index surpassed a previous peak recorded in January 2008, the Office for National Statistics (ONS) said.
Prices were 3.8% higher year on year, with England recording the strongest annual growth at 4.1%, followed by 1.1% in Northern Ireland and 1.0% in Wales, while Scotland saw prices fall by 0.7% over the year typically.
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.
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.
After London, the East and West Midlands recorded the next biggest rises across England, with annual uplifts of 3.8% and 3.5% respectively.
The ONS figures also showed how house prices are picking up in the northern regions as the housing market revival spreads.
The North West and North East recorded annual price rises of 2.3% and 2.2% respectively, only just lagging behind increases of 2.5% and 2.6% in the South East and South West.
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."
A member of the Bank of England's Monetary Policy Committee, which sets interest rates, warned that Help to Buy could force up house prices and said it should not become "a permanent feature of our economy".
Martin Weale warned that house prices are rising "appreciably more rapidly" than might have been predicted, and said there was a risk that Help to Buy will increase upwards pressure by adding to demand while supply of new homes is weak.
In written evidence to the House of Commons Treasury Committee, Dr Weale said: " The extra liquidity offered by the Help to Buy scheme may encourage house-building, but I share the previous governor's (Lord King's) view that it should not become a permanent feature of our economy.
"While reports on the first stage of the scheme suggest that it has had a substantial influence, with 2,000 buyers a month benefiting, this number is small compared with the overall number of housing transactions.
"It was quite possible that demand-side indicators will continue to show further buoyancy. While supply of new houses is also likely to increase, for current levels of loan approvals, house prices are rising appreciably more rapidly than would have been predicted on the basis of the relationship between the two for the period before the crisis.
"There is obviously a risk that, if the mortgage guarantee element of Help to Buy is not priced satisfactorily, it will add to demand while supply is weak, leading to increased pressure on prices."
Dr Weale added: " Rising house prices may make people feel cheerful and more prosperous, thereby supporting household spending. But rising house prices impose a burden on those who do not yet own houses but aspire to in the future. Like government borrowing, rising house prices can crowd out productive investment.
"We are also very aware that developments in the housing markets can pose risks to financial stability. This risk is high if lending is taking place on the basis of poor security or with little margin to spare should prices turn down."
Dr Weale's comments came in a written submission ahead of a Treasury Committee hearing on his reappointment to the MPC for a second term.