The figure is just 0.1% on the 3.7% year-on-year increase to August.
The ONS explains house prices appear to be rising because of a larger annual decrease in September 2012.
The study also shows home prices are growing faster in London than the rest of the UK.
Estate agents also say house prices are rising in the latest survey by the Royal Institution of Chartered Surveyors (RICS).
In a sentiment survey, RICS reveals that 57% of estate agents reported rising prices ' an 11 year high.
Estate agents disclosed a huge increase in new buyers looking for homes is triggering the increase as sellers are holding back from the market.
They add that the government?s Help to Buy scheme is generating inquiries from hopeful buyers who previously could not find a mortgage.
The flipside of more people looking to buy a home is deflating the buy to let rental market. Only 11% of letting agents reported a rise in the number of tenants seeking to rent, the lowest result for a decade.
RICS also says the number of homes sold surged ahead last month ' to an average 20.3 an estate agent. This was the highest level since February 2008.
?It?s no secret the housing market is gathering some momentum and that buyer numbers are on the rise right across the country,' said RCIS chief economist Simon Rubinsohn.
?A greater willingness by lenders to increase loan to values on mortgage products allied to the Help to Buy scheme has meant that more and more first time buyers are in a position to enter the market.
?In spite of this, the amount of homes currently up for sale is still nowhere near enough to keep up with demand and ' in order for the market to function correctly ' this imbalance urgently needs to be addressed.
?Housebuilding starts have picked up recently but we are still well behind in terms of the amount of properties needed. If we are to create a more sustainable market, it is critical that many more good quality homes are built in areas where people want to live.
Article courtesy of LandlordZONE