On an annual basis the rate of house price growth slowed a little, to 3.5% from 3.9%, but Nationwide economists said this was to be expected, as July's figure was flattered by a low base for comparison.
Robert Gardner, Nationwide's chief economist, said: "A number of factors appear to be contributing to the recent upturn in house price growth.
“Consumer confidence has increased significantly in recent months, thanks to further modest gains in employment and signs that the UK economy is finally gathering momentum.
"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 and Help to Buy schemes, is also enabling more people to take their first steps into the property market.”
But Gardner warned that construction must keep up with demand if the markets revival is to be maintained.
He said: "While there have been encouraging signs that house building is starting to recover, construction is still running well below what is likely to be required to keep up with demand.
“New housing starts in England were up 33% in Q2 compared to the same period of 2012, but this is still 36% below the levels prevailing in 2007, which were already below that required to keep pace with household formation.”
"The risk is that if demand continues to run ahead of supply affordability may become stretched.”
“While house prices are still elevated compared with incomes, affordability is being supported by the ultra low level of interest rates.
“A typical mortgage payment for a first time buyer is currently equal to around 29% of disposable income, in line with the long term average.”
“Recent guidance from the Bank of England's Monetary Policy Committee, that it intends to keep interest rates on hold at least until the unemployment rate reaches 7%, may also help support confidence amongst potential buyers.
“However, despite this guidance, there is still considerable uncertainty as to the future path of Bank Rate.
“The Bank of England's central forecast is that the unemployment rate will not reach the threshold level of 7%, but financial market indicators continue to point to a first rate hike in mid-2015."
Jonathan Harris, director of mortgage broker Anderson Harris, added: “House prices continue their steady ascent, driven by increased confidence in the economy generally and rising employment.
“The uptick in prices is also fuelled by the rising number of first-time buyers taking advantage of low mortgage rates, indicating that price rises are not yet deterring them from getting on the housing ladder. However, if prices continue to rise at this pace, it could well become an issue.”
“Government schemes such as Funding for Lending and Help to Buy will continue to support the growing availability of cheap mortgages in coming months, which should fuel further price increases.
“However, once interest rates start to rise there could be plenty of people who find themselves in difficulty so it is important that borrowers take care and ensure they don't overstretch themselves in their desperation to become a homeowner.”