This was the first increase in this measure of the underlying trend since May 2012 following six consecutive falls.
However prices in the three months to December were slightly lower (-0.3%) than in the last three months of 2011.
This marked an improvement over the previous few months and was the smallest annual decline since May 2012 (-0.1%).
Activity has picked up a little according to the index. It shows home sales improved modestly in the second half of the year from 75,000 in July to 80,000 in November.
Overall, sales in the three months to November were 2% higher than in the same period last year (source: HMRC, seasonally adjusted).
Commenting, Martin Ellis, housing economist, said: "There was evidence of a firming in the housing market in the final few months of 2012.
“Prices in the three months from October to December were 0.6% higher than in the preceding three months. This was the first increase in this measure of the underlying trend for seven months.
"Overall last year saw an even mix of monthly rises and falls as prices lacked any real direction as both demand and supply pressures remained largely unchanged during 2012.
"We expect continuing broad stability in house prices nationally in 2013 with prices likely to end the year at levels close to where they begin."
Commenting on the data, Jonathan Samuels, CEO, Dragonfly Property Finance, said: "There was certainly a strengthening in the property market in the latter stages of 2013 although why is anyone's guess. Product competition among lenders and better rates due to the Funding for Lending Scheme and the more stable jobs environment may be drivers.
"Still prices remain down on a year, if only marginally, and this seems to tally with the general lack of direction in the overall market.
"I wouldn't read too much into December's strong showing. Prices have been volatile for some time now, due to low transaction levels.
"Flat seems to be a fairly accurate forecast for 2013 given the inconsistencies and aberrations in the economy. For every positive such as high employment, there is a negative, whether high inflation or a weak services sector.
"Headless chicken is an overused phrase but the property market is unfortunately running around like one.
"Expect continued regional and month-on-month house price volatility during 2013 and for the market, with the exception of prime property, to have remained flat.
"If we enter a triple-dip recession, which now looks possible given last week's services sector data, that could hit consumer confidence hard and apply downward pressure to prices.
“The first quarter of 2013 could set the tone for the entire year."
