House price inflation has risen to its highest rate in nearly a year, according to Halifax, with prices accelerating at an annual rate of 3.7%, significantly above the rate of wage growth.

Britain’s biggest mortgage lender said the price of an average home in the UK hit a record £229,958 in August despite the month-on-month increase slowing to 0.1%.

Its managing director, Russell Galley, said: “A low unemployment rate and a gradual pickup in wage growth are helping to support household finances. This has been accompanied by interest rates still remaining at a historically low rate and a stable, yet constrained, supply of new homes onto the market further supporting house prices.”

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But the Halifax figures show a marked divergence from the other closely watched index of prices, issued by rival mortgage lender Nationwide. Last week Nationwide said its data for August showed the biggest monthly fall for six years, lopping more than £2,200 off the typical house price.

Both lending indices have to deal with a relatively low number of transactions and a two-track UK property market in which activity and prices have stalled in the south but are robust in the north.

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In Leeds, Mark Manning of the estate agents Manning Stainton said: “We experienced the strongest month we’ve had since 2007. The number of properties we sold in August was up by 9% compared with the same time last year and we also experienced an increase in first-time buyer activity, with a 16% increase in inquires compared to the same time last year. The housing market is still in a robust position and prices will keep rising steadily.”

In London, the market is “largely stuck in neutral”, said Jeremy Leaf, an estate agent and a former residential chairman of the Royal Institution of Chartered Surveyors. “Both buyers and sellers need to come to terms with new market realities.”

However, Jonathan Hopper, one of the previously more downbeat commentators on the London market, said there were signs of a fragile pickup in the capital, dampening hopes that prices could fall further.

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“While Britain’s tortuous Brexit negotiations, and the fear of an inconclusive no-deal, still have the potential to deliver a market earthquake, for now the national picture remains one of fragile progress,” said the managing director of Garrington Property Finders.

“Softening prices in London and a few other overpriced areas are slowly improving affordability for aspiring homeowners and creating some attractive buying opportunities. Buyers who had been sitting on the fence are realising prices won’t come to them, and increasingly deciding to take the plunge before interest rates rise further.”

Halifax said the number of first-time buyers entering the market has more than doubled since a record low in 2009 in the aftermath of the financial crisis. The total is now just 8% lower than at the peak of the last boom in 2006, it added.