Martin Ellis, Halifax housing economist, said: "House prices in the three months to October were 1.6% higher than in the previous three months; this rate is below the increases of 2.0-2.1% recorded in each of the previous four months.
“Despite the slowdown in the quarterly rate, the annual rate continued to rise with prices in the three months to October 6.9% higher than in the same three months last year.
"Demand has increased this year, putting upward pressure on house prices and increasing levels of activity. Low interest rates, and higher consumer confidence supported by the increasing evidence that a sustainable economic recovery may now be underway, are helping to increase housing demand. Schemes, such as Funding for Lending and Help to Buy, also appear to have boosted demand.
"Despite increases in the past year both house prices and sales remain below the levels reached at the height of the last housing market cycle in 2006/2007. Sentiment towards selling has also improved in recent months in response to the pick-up in the market, which should help to increase the availability of properties on the market over the coming months."
Joseph Murrock of Wesold.co.uk, the nationwide pay-per-view estate agents, said: "On the surface, this latest data from the Halifax will add to concerns of another house price bubble. The three-month growth figure may have slowed but the overall market continues to rise.
"But the fears of a bubble are being overplayed in many areas of the UK.
"In many areas of the UK, as the Halifax reminds us, house prices remain significantly below their 2007 peak. In some areas, they're still falling. For anyone inside the M25, this is easily forgotten.
"London is at risk of overheating, few can realistically deny that, but what's happening in the capital is hugely distorting the image of the broader UK market.
"Funding for Lending, Help to Buy, a recovering economy and rising consumer confidence are all driving the market forwards.
"The fact that home sales are up 21% relative to the same three months of last year underlines this confidence. With loans so cheap, people have finally come out of their shells.
"If the recovery of the property market is to be sustainable, the supply of new houses needs to be addressed. This is especially the case in the capital.
"Where supply is constrained, the property market is like a leveraged trade. Its growth rate amplifies the real growth rate in the economy and underlying market conditions.
"If prices continue to rise in London, this will certainly need to be addressed, potentially via a new tax on foreign property investors.
"If things continue as they are in the capital, you get the feeling there is only one end result."