The Bank of England has lent banks and financial institutions £10bn in a move analysts expect to ease the impact of a credit crunch and high borrowing costs.
The Bank is one of five central banks that have pledged emergency cash to stop credit markets seizing up.
Borrowers bid for the cash at auction, with those who bid at the minimum rate of 5.36% getting 75% of the amount they had requested.
Demand for the money was less than many analysts had expected.
However most banks had to pay above base rate for the loans.
Total bids exceeded the £10bn on offer by £850m with the highest accepted rate being 6.6% - giving a weighted average rate of 5.949%, the Bank said.
"The rate was low and demand was relatively low which suggests that pressures might not be as intense as we perhaps might have thought," said John Wraith, head of UK interest rate strategy at Royal Bank of Scotland.
"Someone borrowed money at 6.6% and that definitely suggests that they were desperate to get some funding," he added.
In London, the three-month sterling Libor rate - at which banks lend to one another - dropped for a fourth session on Tuesday after the bank's auction, signalling that the central banks' rescue plan may be having an impact.
The Libor, which stands for the London Inter-bank Offered Rate, dipped to 6.386%, compared with 6.627% on Wednesday last week when the central banks unveiled their rescue plan.
The lower the rate, the cheaper it is for banks to borrow money.
But Bank of England governor Mervyn King said banks were still deeply concerned about the liquidity crunch.
"A painful adjustment faces the global banking sector over the next few months as losses are revealed and new capital is raised to repair bank balance sheets," Mr King told MPs on the Treasury Select Committee.
'No silver bullet'
Under the auction rules, the £10bn was lent for three months.
Mr Wraith said that one reason for the relatively low demand could be because some UK financial institutions may have sought cheap funding from the European Central Bank.
Global financial markets have been dealing with a number of problems
On Tuesday, the ECB allocated 348.67bn euros ($502bn; £249bn) to banks at a below-market rate of 4.21%.
It had said that more money would be offered if needed.
The aim of the cash auction was to cut the cost of lending between retail and commercial banks, which has jumped in the past few weeks.
It had remained stubbornly high despite interest rate cuts in the UK and US.
Should the borrowing costs stay high, then this may end up being passed on to consumers, slowing economic growth.
"The central banks have made sure they'll be no year-end problems in money markets, but it doesn't mean there won't be problems in the new year," said Mr Wraith.
Demand for money rises toward Christmas as companies and financial institutions do end-of-year accounts.
On Monday the US Federal Reserve made $20bn available through auction, though it did not say how many banks took advantage of the extra money.
The national banks of Canada and Switzerland are also involved in the plan which will together see the banks inject at least $600bn.
US Treasury Secretary Henry Paulson said on Monday that there was no "silver bullet" to solve the credit market problems.
The main reason banks have been unwilling to lend to each other is a downturn in the US property market.
A surge in mortgage defaults and bad debts has forced many banks to cut the value of their mortgage investments, costing them billions of dollars.
As a result, the banks fear that they might need any spare cash they have to cover their losses.