Lenders approved 36,115 home loans in December, the weakest level since April 2013.
The figure was 19% down on the same month a year before and also weaker than the 39,007 level seen in November, UK Finance said.
Meanwhile, annual growth in consumer credit slowed, from 0.8% to 0.7%.
It comes as households grapple with falling real-terms wages – as pay growth fails to keep pace with a rise in the cost of living – and also digest the impact of November’s Bank of England interest rate hike, the first in a decade.
Lenders have reported a slowdown in national house price growth in 2017, dragged down by falling prices in London.
Samuel Tombs, chief UK economist at Pantheon Macroeconomics, said the latest data showed mortgage approvals “falling off a cliff”.
He said: “The deterioration in consumers’ confidence, driven by the squeeze on real incomes and the November interest rate hike, has taken a heavy toll on the mortgage market.”
Mr Tombs suggested that the Bank of England had “seriously misjudged the ability of the housing market to withstand even modest increases in interest rates”.
Howard Archer, chief economic adviser to the EY ITEM Club, said 2018 looked likely to be a “challenging year for the housing market”.
He said activity was “likely to be lacklustre as the squeeze on consumer purchasing power only gradually eases, confidence remains fragile and caution persists over engaging in major transactions”.
The figures come as housing industry data shows the number of new home starts in the UK rose to its highest level in a decade last year.
A total of 160,606 homes were registered in 2017, up 6% on the year before and the highest since before the financial crisis in 2007, when the figure stood at 198,929, the National House Building Council (NHBC) said.
New home completions were also up, climbing 4% to 147,278, the highest level since 2008.
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The report also sounded a positive outlook for building this year.
Theresa May is targeting an increase in the construction of new homes to 300,000 a year to address Britain’s shortage of housing.