House prices rose by 1.1% during July as the property market appeared to gather momentum.
Figures from the Halifax were the second rise in the past three months.
It leaves prices in the three months to July 0.8% higher than in the previous quarter.
So far this year, house prices have fallen by less than 1%.
Halifax housing economist Martin Ellis said: "Demand for homes has risen, albeit from a very low base, since the start of the year, driven by improvements in affordability and low interest rates."
The Halifax said prices were now 12.1% lower on a year earlier, with an average price of £159,623.
The figures extend the recent positive trend after building society Nationwide reported that the average value of a UK home rose by 1.3% in July.
And the number of mortgages approved for house purchase has also risen for five months in a row to the highest level for more than a year.
IHS Global Insight economist Howard Archer said it was possible that April marked the trough in house prices on the Halifax measure.
But he warned much uncertainty remained in the market.
He added: "We suspect that they will be prone to relapses over the coming months and we certainly do not think that a sharp sustained upward trend in house prices is in the process of developing."
Mr Archer said it continued to be very difficult for many people to get mortgages - particularly first-time buyers - and this situation was likely to improve only gradually.
As well as stronger demand, the market has been supported by a record low Bank of England base rate of 0.5%.
This is expected to remain unchanged when the Bank's monetary policy committee announces the outcome of its monthly meeting tomorrow.
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