Prices rose 1.9 per cent year-on-year in June to £168,941, up from £165,738 a year earlier.
On a monthly basis, prices rose 0.3 per cent, up from £167,912 in May.
Nationwide chief economist Robert Gardener says: “The annual rate of house price growth increased to 1.9 per cent in June – the fastest pace since September 2010. A number of factors are likely to be contributing to the recent acceleration.
“Demand for homes has been supported by further modest gains in employment, as well as an improvement in the availability and a reduction in the cost of credit, partly as a result of policy measures, such as the Funding for Lending Scheme. Signs of a modest improvement in wider economic conditions may also be playing a role in boosting buyer sentiment.”
The strongest performing regions continue to be in the South of England, especially London.
The South East experienced a 2 per cent annual growth in house prices, from £197,564 in the second quarter of 2012 to £202,132 a year later.
London grew 5.2 per cent year-on-year, from £302,399 in Q2 2012 to £318,214 in the same quarter a year later, meaning London’s house prices grew about 3.5 times faster than the rest of the UK.
Year-on-year house prices increased 1.2 per cent in Wales, from £131,840 in Q2 2012 to £133,432 a year later. In Scotland, prices fell 1.1 per cent from £136,182 to £134,432 over the same period and, in Northern Ireland, prices fell 2 per cent from £110,422 to £108,116.
Prices are still around 9 per cent below their pre-crisis peak. However, London prices reached a new all time high, 5 per cent above the £303,739 they reached pre-crisis.
House prices in England are currently 5 per cent lower than their 2007 peak, while they are 13 per cent lower in Wales, 12 per cent in Scotland and 53 per cent in Northern Ireland.