The supply of properties for sale is severely limited in some areas
Growth in house prices in England and Wales slowed in December, according to property website Hometrack.
It said the average cost of a home rose by just 0.1% to £156,900, as the number of house-hunters fell by 2.2%.
Spokesman Richard Donnell said slow growth in household incomes and unemployment would curb demand in 2010.
Hometrack said house prices would fall by 1% next year, but the Centre for Economics and Business Research (CEBR) predicted a rise of between 2% and 4%.
Latest figures from the Halifax, one of the UK's biggest mortgage lenders, suggested that prices rose by 1.2% in October.
The CEBR said it expected prices to be about 15% higher at the end of 2012 than they are today.
The BBC's Joe Lynam said house prices in much of the UK had risen modestly, but steadily for most of this year, buoyed by record low interest rates, limited supply and better than anticipated employment levels.
However, Hometrack suggests this trend has slowed in December, although this is in part due to the traditional seasonal slowdown as potential buyers put off house-hunting until after Christmas.
The number of new buyers entering the market fell for the first time in 11 months and only 11% of postcodes saw price increases during December, down from nearly 18% in November.
Hometrack says house prices are now 1.9% lower than they were a year ago and will fall by a further 1% by this time next year due to limited demand.
Mr Donnell said: "Unexpectedly buoyant demand and a chronic lack of housing for sale were the key drivers of the housing market in 2009.
"While a scarcity of housing is set to remain an important feature of the market in 2010, it is the prospects for demand that will dictate the outlook for prices in the next 12 months."
Hometrack collects data from 3,500 estate agent offices from all 2,200 postcode districts in England and Wales.
They reported a 41% increase in demand during the past year, with a rise of 70% in London.
But the number of properties for sale has risen by only 7% during the same period and in south-east England there was actually a fall in availability.