December's fall follows a 3.2 per cent decline in November, with further drops possible in 2011 when Rightmove predicts a decrease of as much as 5 percent for the year if property repossessions pick up.
Property prices do normally slip in the winter months and the Rightmove survey is not seasonally adjusted.
But mortgage lenders Nationwide and Halifax have reported falling house prices for November too, in a sign a modest downturn in Britain's property market could become entrenched as looming government spending cuts curb appetite for houses.
"In 2011 we will see larger falls in weaker markets due to over-supply and forced sales," said Rightmove director Miles Shipside.
"The net result is likely to see average national asking prices fall slightly," he continued. "At best they could be close to flat and at worst down by five per cent if repossession numbers jump up from 1 in every 15 sales."
Rightmove said recent price falls and some nervousness about prices in 2011, plus growing arrears, could result in lenders increasing the number of repossessions.
"If (Bank of England) base rates increase then repossession numbers could form a much larger percentage of total sales, and at an extreme this could lead to even greater price falls than we are forecasting," it said.
Most economists do not expect the BoE to raise interest rates until late 2011 at the earliest because of uncertainty about the economic impact from the start of a four-year program of government spending cuts.
Rightmove said it expected properties coming to the market to fall to around 1.2m in 2011, down around 10 per cent on 2010 and 40 per cent below the historically normal figure.
The website said that an early sign of the weak supply of properties was the fact that the number of new properties for sale this December was only 0.1 per cent higher than a year ago.
That was despite a reduction in the legal paperwork required to market properties earlier in the year, which Rightmove had expected to result in more speculative sellers in the market.
Estate agents reported that mortgage funds remained difficult to arrange following a further tightening in lending criteria in the middle of 2010.
And the time properties spent on the market remained near last month's record high while the unsold stock per estate agency branch was at 74, down from 77 in November but still traditionally high.