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Growth in UK house prices sped up in the year to October, says the country's largest mortgage lender, because of "improving economic conditions".

The Halifax said that prices rose at an annual pace of 9.7% last month - up from 8.6% in September.

During October itself, house prices rose by 1.1%, following a decline of 0.9% in the previous month.

The increase brought the average price of a flat or house across the country up to £205,240, a record high.

Martin Ellis, Halifax housing economist, said: "Improving economic conditions and household finances, together with sustained low mortgage rates, have boosted housing demand during 2015.

"Strengthening demand is filtering through into higher sales levels, although the ongoing shortage of supply is acting as a significant constraint on activity."

He added that demand was likely to outstrip housing supply over the coming months, "maintaining upward pressure on house prices".

This lack of supply has caused problems for estate agent group Countrywide - whose brands include Hamptons and Bairstow Eves. On Wednesday, it warned that its full-year profits were expected to fall as a result of fewer properties coming on to the market.

The company said that "the anticipated post-election recovery in residential transactions failed to materialise in any significant way".

Last week, rival mortgage lender Nationwide said house prices rose by 3.9% in October from a year earlier.

Property values were up by 0.6% compared with September, the building society said, putting the cost of the average home at £196,807.