At the start of this year, Rightmove had forecast that sellers' asking prices would rise by 2% across 2013, but it now believes that prices are set to rise by around 6%, after previously raising its prediction to 4% a few months ago.
Rightmove said that asking prices fell by 1.5% month-on-month in September to £245,495 on average, marking the second monthly fall in a row, with a slightly bigger 1.8% drop seen in August.
But prices are still 4.5% higher than the same period a year ago and have increased by around £16,500 since the start of the year.
Last week, the Royal Institution of Chartered Surveyors (Rics) suggested that a 5% cap should be placed on annual house price growth to stop any future house price bubble and borrowers taking on too much debt for fear of missing out on a boom.
Much of the increased demand from buyers which is helping to push house prices up has been put down to Government stimulus schemes such as Funding for Lending and Help to Buy.
The only two regions in England and Wales not to see an annual increase in prices in September were the North, where prices were flat, and Yorkshire and Humberside, which saw a 1.3% fall. East Anglia saw the smallest annual increase at 0.8%.
Prices rose by 1.3% year-on-year in the South West, by 1.7% in the North West and by 2.9% in the East Midlands.
In general, prices have already started to see a "turnaround" in the last couple of weeks as the autumn season kicks in according to the website, which also said that traffic was up by one fifth on last year.
Market activity traditionally slows down around the summer holiday period and sellers price their properties keenly to tempt buyers into a deal. Rightmove said the volume of sellers coming onto the market this month is the lowest it has seen since February.
But the increased demand from would-be buyers at a time when there is a lack of choice is likely to "prime the pump" for a price surge this autumn in some sectors of the market, Rightmove said.
Lenders have recently reported that first-time buyers have returned to the market in their largest numbers in more than five years.
Some experts have urged the Government to consider ditching the controversial second phase of Help to Buy which is set to launch next year with a guarantee scheme to help people with low deposits where the state takes on the risk of a borrower defaulting.
But others have said that talk of a property boom is premature, with the strength of the housing market still varying widely across many areas of the UK.
Miles Shipside, Rightmove director, said: "The autumn market is set to heat up as the weather cools down following the summer lull in fresh property supply.
"While prices fell during the month overall, the last couple of weeks have seen the start of a turnaround, with more sellers choosing to come to market and pitching at higher prices as momentum rebuilds."
Mr Shipside said some buyers with decent deposits might try to snap up a property this autumn, before Help to Buy increases competition further among buyers for properties from next year.
He said: "We forecast the national average increase in new seller pricing for the whole of 2013 to be in the region of 6%, partly driven by the strength of southern markets but increasingly contributed to by the more buoyant areas of the north."