British house prices rose strongly in 2013, bolstered by rapidly falling unemployment, greater economic confidence and schemes from the government and the Bank of England to revive mortgage lending and construction after the financial crisis.

But Halifax, part of Lloyds Banking Group, said property prices finished the year on a weaker note. House prices dropped by 0.6 percent in December, causing the year-on-year rate of house price growth to slow to 7.5 percent from November's six-year high of 7.7 percent.

None of the economists polled by Reuters before the data said they had expected a monthly fall in house prices. Halifax revised down November's price increase to 0.9 percent from an initial estimate of 1.1 percent.

Halifax's data also showed slower growth than data from rival mortgage lender Nationwide, which reported a 1.4 percent rise in house prices in December to give an annual increase of 8.4 percent, the biggest in more than three years.

However, Halifax said it still expected house prices to rise in 2014 by around 4-8 percent, and some economists think they could rise faster.

"There is still a very real risk that a new housing bubble could really develop in 2014, especially as there is mounting evidence ... that the strength in house prices is becoming widespread," said Howard Archer, chief UK economist at IHS Global Insight, who expects prices to rise 8 percent.

The government was criticised by many economists for extending its Help to Buy scheme in October to make it easier for home-buyers to get mortgages with a 5 percent deposit, something the government hopes will spur construction.

In November, the BoE announced it would scrap the aspect of its Funding for Lending Scheme that offered banks cheap finance if they increased mortgage lending.

Central bank data for that month showed lenders approved the greatest number of mortgages since 2008.

But Halifax does not expect prices to get out of control because weak wage growth should limit buyers' purchasing power.

"Continuing pressures on household finances, as earnings again fail to keep pace with consumer price inflation, are expected to constrain demand," its housing economist Martin Ellis said.

In another sign of the fragility of consumer demand, data from the British Retail Consortium released earlier on Wednesday showed that high-street stores were engaged in the biggest pre-Christmas discounting on record.

Halifax said the average property price was 173,467 pounds ($284,500) in December, equivalent to 4.7 times average annual earnings for a full-time male employee.

Ellis added that recent price rises were also likely to tempt more home-owners to sell, boosting supply and limiting further price gains.

(Editing by William Schomberg; Editing by John Stonestreet and Elizabeth Piper)

By David Milliken