There were 32,288 mortgages approved for house purchases during the month, down on December and 14% lower than January 2012.
The British Bankers' Association (BBA) also said that loan and overdraft repayments outstripped new borrowing.
Ongoing problems in the eurozone, regulatory changes, and rising costs in the wholesale markets will constrain the supply of funding. The biggest single factor is the trend towards deleveraging as lenders come under greater pressure to increase their capital reserve ratios.
The demand for mortgages remained weak in 2012 because of low consumer confidence, concern over the state of the economy, and the cost and availability of lending. A combination of a shortage in supply and lacklustre demand means that gross lending looks set to remain depressed over the short and medium term.
Key demand-side and supply-side factors continued to deteriorate in 2012, heightening the need to analyse the outlook for the mortgage market. A lack of funding will restrict the ability of providers to increase lending, and demand will be adversely affected by low consumer confidence.
A report by pensions and investments company Scottish Widows, published on Monday, claimed that many people were living on a "financial precipice", with little or no savings to fall back on.
A survey, based on responses from 5,000 people, found that 31% of respondents said they were not currently placing any cash aside, although this was a slightly smaller proportion than a year ago when it stood at 32%.
Only 11% of those surveyed expected the economy to pick up this year and 17% had no money to fall back on at all, the report said.
For more information on the UK mortgage market, see the latest research: UK Mortgage Market
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