Property values were pushed up by 0.8 per cent month-on-month, marking the 16th monthly increase in a row, and the annual pace of price growth accelerated from 10.6 per cent in July as a result.
Typical UK house prices first surpassed their 2007 peak in cash terms in May this year and they have been hitting new records every month since.
Year-on-year house price growth has been in double digits since April, according to the building society's study.
Despite property values reaching record highs over the summer, there have also been signs of a cool down in the market in recent months.
Mortgage approvals generally dipped after stricter lending rules, which force lenders to ask for more detail about a mortgage applicant's spending habits, came into force at the end of April but approvals have since rebounded slightly.
Nationwide said it is still unclear how much of the cooling in activity was due to the introduction of the new Mortgage Market Review (MMR) rules as opposed to an underlying loss of momentum in the market.
Robert Gardner, Nationwide's chief economist, said that while house price growth continues to outpace earnings by "a wide margin", cheap mortgage rates mean that, at present, typical mortgage payments as a share of people's take-home pay are relatively affordable.
And speculation about the possibility of the Bank of England base rate moving from its historic 0.5 per cent low has prompted calls for homeowners to start preparing now for how they will cope with higher borrowing.