The figures, published yesterday by the British Bankers' Association (BBA), showed that the stock of lending to non-financial companies by the big UK banks fell by a net £246 million in January to £288.2 billion. This followed drops of £3.1bn in both November and December.
The BBA figures include lending by Royal Bank of Scotland, Lloyds Banking Group, Barclays, HSBC and Santander UK.
The average monthly decline in lending to non-financial companies over the six months prior to December was £1.4bn, according to the BBA figures.
The further fall in lending in January casts doubt on the extent to which the Bank of England and UK Government's Funding for Lending (FLS) scheme is boosting lending to businesses.
This £80bn scheme, launched last summer, offers funding to banks at below-market rates, with financial incentives to encourage them to lend.
Howard Archer, chief UK economist at consultancy IHS Global Insight, said: "While there was a much-reduced fall in net lending to non-financial companies in January, there remains little evidence that the (FLS) is having any material impact in lifting bank lending to companies."
But he believed lending was being depressed not only by issues with supply of finance but also by reduced demand from some firms.
He said: "It needs to be borne in mind low lending levels to companies have reflected weak demand as well as supply factors.
"There is clearly low demand for credit, with many companies wary about borrowing and investing in the current difficult economic environment.
"Furthermore, many companies are looking to pay down debt."
UK gross domestic product fell by 0.3% in the fourth quarter of 2012. A further drop in the current quarter would see the UK record its third recession since 2008.
International agency Moody's on Friday downgraded the UK's sovereign credit rating from triple-A to Aa1, citing weak prospects for the economy. The pound fell sharply yesterday against the dollar and euro.