According to the index house prices grew 0.3 per cent from August, making the average home worth £206,015.
Prices have slowed both on an annual and a monthly basis. Growth in August was 0.6 per cent while prices in September are up 5.3 per cent on an annual basis compared with the previous month, when growth was 5.6 per cent.
Robert Gardner, Nationwide’s chief economist, said growth remains within the 3 per cent to 6 per cent range it has been in since early 2015.
He said: “The relative stability in the rate of house price growth suggests that the softening in housing demand evident in recent months has been broadly matched on the supply side of the market.
“Survey data indicates that, while new buyer enquiries have remained fairly subdued, the number of homes on the market has remained close to all-time lows, in part due to low rates of construction activity.
“The number of new homes built in England has picked up, but is still not sufficient to keep up with the expected increase in the population.”
In the four quarters to Q2 2016, 139,000 new houses were completed, 30 per cent higher than the low point seen in 2010.
But this is still around 15 per cent below the average rate of building in the five years before the financial crisis and 38 per cent below the 225,000 new households projected to form each year over the coming decade.
Figures from the Council of Mortgage Lenders show a drop in the number and value of transactions since Britain's vote to leave the European Union in June but the trade body has said it is hard to tell whether this is a direct reaction to the vote, or the continuation of a market already cooling.
Meanwhile Bank of England figures show mortgage approvals fell in August for the third month in a row.
Unsurprisingly the region with the highest average house prices was London, where a home will now cost £474,736 on average.
This has increased by 7.1 per cent during Q3 2016 but the region with the highest price growth has been the Outer Metropolitan area, where prices grew by 9.6 per cent, meaning the average home costs £358,153.
Meanwhile house prices in the North region are the lowest on average at £124,074 and fell by 0.2 per cent during the quarter.
Mr Gardner said: “There were tentative signs of a convergence in house price growth amongst the English regions.
“Most southern regions saw a slowing in annual price growth compared with Q2, while a number of northern regions, such as the North West, saw a pick-up in growth.
“Nevertheless, it remains the case that prices in Southern England are well above pre-crisis levels, while those in the North, North West and Yorkshire & Humberside are still below their 2007 peaks.”
Mark Harris, chief executive of mortgage broker SPF Private Clients, said that despite the rise in house prices there should be a glut of good deals for borrowers.
He said: “Falling swap rates continue to encourage lenders to reduce mortgage rates, which has meant a busy September for the mortgage market.
“Remortgaging numbers are high as people take advantage of cheap rates and rising equity in their homes to release some extra cash to fund a renovation or extension, rather than go to the extra cost of moving.
“With lenders keeping one eye on end-of-year lending numbers, we expect to see the continuation of competitive deals well into the autumn, which is great news for buyers and those remortgaging alike.”
