Banks and building societies have shown no interest in borrowing up to £10bn of Bank of England funds.
The Bank of England is making three-month loans available
There were no bidders for the money in the Bank's auction, which was held to ease strains in the money markets.
It was the first such auction in the Bank's history and was designed to ensure lenders did not face the kind of funding crisis that hit Northern Rock.
But a Bank of England official admitted that at a minimum lending rate of 6.75%, the loans were "expensive".
The Bank defended its decision to hold the auction, calling it a "safety valve in the light of concerns that arose about potential pressures in the banking system more generally as a result of Northern Rock".
But it added: "Since the announcement, there has been a significant fall in three-month interbank rates which made the auction look expensive."
Despite the lack of demand, the Bank confirmed three more planned auctions would still go ahead, with the next one due on Wednesday 3 October, the one after that on 10 October and the final one on 17 October.
But BBC business editor Robert Peston believes any hopes that the Bank will replace the minimum interest rate of the base rate plus one percentage point for a market rate will be dashed.
And as a result, he says the "funds are attractive only for banks with the financial equivalent of devastating BO and which find it hard to raise funds from other banks".
"However it makes sense for the Bank to offer the money again in coming weeks, just in case the BO is a symptom of a rather more worrying condition."
The Bank of England announced its offer of three-month loans at the height of the crisis surrounding Northern Rock on 19 September.
At the time, the three-month inter-bank interest rate, or Libor, which is the rate banks borrow money from each other, had risen way past the Bank of England's base rate of 5.75%. It was even more expensive than the Bank's emergency lending rate of 6.75%.
This suggested that banks were reluctant to lend money to each other because of various uncertainties in the financial system rooted in the US sub-prime mortgage crisis.
In recent months, many people on low incomes or with bad credit histories who have taken out mortgages have been unable to repay them because of steeper interest rates.
In addition, it emerged that major banks across the US and Europe were affected by this because they had been investing for years in bundles of debt which had included these sub-prime loans.
However, the Libor rate has dropped sharply in the past week or so, now hovering at about 6.34%, which means the wholesale money markets appear to be starting to return to normal after the recent turmoil.
For this reason, analysts speculated that banks would be wary of putting in a bid for a Bank of England loan because of the stigma attached to drawing on the funding at a comparatively punitive rate.
Over the past month, the Bank has made available more than £20bn of funds for banks to borrow for periods lasting up to a week.
This was to cover shortfalls in their reserves, rather than to bail out lenders who had allowed themselves to get burned by the fallout in the US sub-prime meltdown.
The auction on Wednesday was the first such measure taken by the Bank of England specifically to tackle the log-jam in the credit markets and so helping to repair the damage to British savers' perceptions of UK banks.
It was widely regarded as a policy U-turn, a step change to the Bank Chairman Mervyn King's previous tough stance on lenders who had lost out from relying on cheap debt over the last few years to aggressively grow their businesses.
However, the US Federal Reserve and European Central Bank have held a number of such auctions in recent months.