The study said Government efforts to boost lending, which include a multibillion-pound scheme launched in August, are likely to have contributed to a pick-up in home sales and house prices.
Martin Ellis, housing economist at Halifax, said that despite the signs of improvement, the tough economy and the pressure on household finances will continue to weigh down on housing demand. He said: "Overall, we expect continuing broad stability in house prices nationally in 2013."
With average house prices standing at £162,932 in January, Halifax also pointed to recent increases in mortgage approvals to home buyers which have been reported by the Bank of England as an indication of what is to come.
Mortgage availability has increased and lenders have been slashing their rates since the Government introduced the Funding for Lending scheme, which aims to boost borrowing by households and firms by giving lenders access to cheap finance.
However, Howard Archer, chief UK and European economist for IHS Global Insight, said that despite the recent signs of improvement, housing market activity is still "muted" by longer-term standards. He said that although there were more than 55,000 mortgage approvals for house purchase in December, marking the highest number in almost a year, this is still way below the average of more than 85,000 approvals a month seen over the last 20 years.