The average house price in the UK in December was £160,063, down 0.9% from November and down 0.1% over the previous quarter.
Martin Ellis, housing economist at Halifax, said: “If the UK can avoid recession, we expect broad stability in house prices in 2012.
“There is however considerable uncertainty regarding the prospects for the UK economy which will, to a large extent, depend on how events in the eurozone unfold.
“In addition, the extent to which households choose to reduce their debts will also affect growth.”
House prices had risen last year by just 1% according to Nationwide.
Yesterday the Bank of England warned that lenders were preparing to tighten down on lending criteria during the first few months of 2012.
They told the Bank they were worried that falling house prices may undermine the security of the loans they had made and were concerned about the worsening state of the economy and its impact on the ability of borrowers to repay.
