The Bank of England said 52,410 mortgages were approved last month.
That was nearly three thousand more than in July, and the highest number since December 2009.
The figures suggest that a recent slight relaxation in lending criteria by banks and other lenders will lead to higher sales in the coming months.
Adrian Coles, director-general of the Building Societies Association, said: "Approval figures continue to look promising as consumers take advantage of the competitive mortgage rates.
""However, the outlook for the economy has deteriorated over the past month as has consumer confidence, which could well spill into the housing market, causing further weakness," he warned.
Lending squeeze Continue reading the main story “ Start Quote We are telling people to be realistic.
If the price is right then it will sell” End Quote David Sharpe, Sales negotiator, Dowen estate agents, Hartlepool UK house prices 'treading water' Average house prices have been stagnant across the UK this year, with both the Nationwide and the Halifax reporting little change in the past few months.
In its latest survey, the Nationwide said house prices had continued to "tread water" in September.
House prices rose by 0.
1% in the month, Nationwide said, but were 0.
3% lower than a year ago.
The number of house sales fell in August, according to the Bank of England's own figures published last week.
They dropped by 6,000 from July to 78,000 in August which was, in turn, 3,000 lower than in August last year.
Approvals are traditionally a good indicator of near term trends in sales, so the latest approvals data suggests that sales funded by mortgage borrowing may pick up this autumn.
But on Wednesday the Bank of England said banks had told it they may face a renewed squeeze on their ability to lend.
In its quarterly Credit Conditions Survey, the Bank said it had been told by some big lenders that they might find increasingly hard to raise the necessary funds on the wholesale financial markets to lend to home buyers.
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