House prices rose by 1.1% in January, according to the latest house price index from Halifax.
The increase follows a 0.5% decline in December, as demand from buyers picks up.
The Halifax's latest monthly index, which is based on mortgages approved by the bank, put the average price of a UK home at £175,546. This is almost £2,000 higher than at the end of 2013.
Halifax said the annual rate of inflation, which it calculates by comparing the average over three months with the average over the same period of the previous year, fell to 7.3% from a recent peak of 7.7% in November.
Martin Ellis, housing economist for the Halifax, said: "With the supply of properties being slow to respond to more buoyant market conditions, stronger demand has resulted in continued upward pressure on house prices.
"Demand has increased against a background of low interest rates and higher consumer confidence underpinned by signs that the economy is recovering and unemployment falling faster than expected."
Nicholas Ayre, managing director of homebuying agency Home Fusion, said the house price growth means buyers are considerably more optimistic than they were this time last year.
“We have broken through the one million transaction threshold for the first time since 2007, which we always see as the darkest days and has come to represent our reference point when everything went horribly wrong. We are moving way beyond that now. We have reached a point at which buyers are now thinking very hard about taking the plunge and this may now be starting to temper demand. The spectre of overpaying and the thought of negative equity could well be in the back of people’s minds,” he said.
“The definition of a house price bubble, is when people will pay anything for a property. This is not what we are seeing here. Many people are still heavily indebted, particularly if they have maxed out on credit cards. Growth at 1.9% over the previous three months and annual price growth falling slightly when compared with the previous month, is hardly a market running away with itself.”