The number of new mortgages approved for house buying rose very slightly in January, to 74,000 from 72,000 in December, the Bank of England has said.
Sales and mortgage borrowing have slumped in the past few months
However, apart from the figure for December 2007, January's level was still the lowest since September 1995.
Mortgage approvals are a good indicator of medium-term trends in sales.
Alongside other borrowing and house price data, they suggest the UK property market will be very subdued in the coming months.
"Demand for, and supply of, credit in the UK mortgage market remains very weak, and is set to ease further going forward," said George Buckley of Deutsche Bank.
All the regular surveys from lenders, surveyors and government bodies have shown that prices have slowed down sharply since last summer.
The Nationwide building society's latest monthly survey suggests that prices have now fallen for four months in a row, the first time that has happened since 2000.
"The modest rise in mortgage approvals in January may dilute some of the deepest pessimism about the housing market," said Howard Archer at Global Insight.
"[But] the Bank of England and Nationwide indicate that housing market activity and price are continuing to suffer from the combined pressures of stretched affordability and tighter lending conditions," he added.
Other figures from the Bank show the total amount of money outstanding on mortgages has now risen to £1.19 trillion.
Taken together with other borrowing, such as bank loans and credit cards, this means that the total amount of personal debt in the UK has now risen to more than £1.4 trillion.
Building societies still appear to be benefitting from the fallout from the Northern Rock crisis.
There was a further inflow of £597m into their savings accounts during January, according to the Building Societies Association (BSA).
Although that was much less than the large inflow of £1.89bn seen in December, it was still the highest January figure recorded since 1997.
By contrast, in January last year building society members took a net £196m out of their savings accounts.
"The January figures often show a net outflow as families pay off Christmas bills, with seven of the previous 10 years seeing net withdrawals," said the BSA's director general Adrian Coles.
"Placed in this context, the savings inflow in January was particularly high," he added.