A total of 36,997 homeowners had their mortgages approved, the British Bankers' Association (BBA) said.
That is the lowest figure since January 2015, and a 21% drop on August 2015.
The number of people borrowing to buy a house or flat has been falling since April, when there was a rush to buy property ahead of stamp duty changes.
"Mortgage borrowing is growing at a slower pace than it has for the last few months reflecting both the slowdown in housing market growth after the April spike and broader trends in the sector," said Rebecca Harding, chief economist at the BBA.
The figures do not include lending by UK building societies, which account for about a third of mortgage borrowing.
However, UK consumers are continuing to borrow more through loans and overdrafts.
The total amount of consumer credit grew by 6.4% in the year to August, the fastest rate of growth for nearly 10 years.
"Given the low interest rate environment and high levels of confidence during the summer, the strong credit growth can be interpreted as strong consumer sentiment," said Ms Harding.
Economists said consumer confidence had recovered since the vote to leave the European Union.
"Consumers were clearly prepared to continue borrowing and spending in August, and it is notable that confidence recovered to a significant extent after slumping in July in the immediate aftermath of the Brexit vote," said Howard Archer, chief European and UK economist at IHS Global Insight.
However, he predicted that such confidence could run out of steam in the months ahead.
"Consumers are likely to face diminishing purchasing power over the coming months as inflation rises and earnings growth is limited by companies striving to limit their costs."
He said unemployment was likely to rise, and predicted that inflation could hit 3% by the end of next year.