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UK house prices in September rose by 3.2% compared with a year ago - the fastest rate for nearly two years, according to the Nationwide.
The building society said that annual growth was highest since November 2022, with terraced homes driving the increase.
It said rising incomes and the expectation of falls in interest rates were improving affordability for buyers.
The average UK house price in September was £266,094, it said.
The latest survey comes as competition has intensified between lenders in recent months.
Brokers say that providers have been offering the best deals to new, house-purchasing customers, rather than those who are remortgaging.
Nationwide, which is the UK's largest building society, recently announced new borrowers could request a mortgage up to six times of their total income with a 5% deposit, but it would only be available for those taking out a five or 10-year fixed-rate deal.
Other lenders have also been lowering the rates of interest they charge.
However, the cost of a mortgage deposit, as well as the monthly repayments, remain major hurdles for potential first-time buyers trying to buy a home.
House prices have been relatively stagnant in the last year, as activity in the UK housing market has been limited.
But many commentators suggest, with interest rates expected to fall, demand from buyers could now pick up.