Gross mortgage lending fell 13% to an estimated £9.2bn in January from £10.6bn in December, as the market shows little signs of rebounding, according to the CML.
Its latest figures revealed lending in January was up 5% compared to the same month in 2010, which is the first year-on-year increase since August 2010.
However, the CML points out comparisons with the beginning of last year are distorted by the continued effects of the Stamp Duty holiday that finished at the end of 2009.
Peter Charles, economist at the CML, says: "The Bank of England's inflation report noted that the UK banks face a significant funding challenge over the next couple of years.
"In total, including funding supported by the public support schemes, around £400bn to £500bn of wholesale term debt is due to mature by the end of 2012.
"This implies that, even in the unlikely event of a marked upturn in mortgage demand, the level of activity in the mortgage market can be expected to remain constrained."
He says the availability of funding for mortgages should improve to more normal levels as the financial market stabilises.
However, Charles adds: "The unprecedented expansion of wholesale funding, and hence mortgage lending, experienced in the mid-2000s is unlikely to return."
In the CML's latest market commentary, Charles notes 2010's figures for transactions, house price growth, gross and net mortgage lending all pointed towards a stabilising market with no evidence for significant change in 2011.
He says: "The lack of impetus in the mortgage market reflects the sluggish state of the economy as a whole.
"While the unexpected fall in GDP in the fourth quarter of last year can be explained by the impact of the freezing weather through most of December, the signs from the early weeks of the new year are that there will be little rebound in activity in Q1 2011."
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