Barclays and Royal Bank of Scotland (RBS) are among those pushing up rates, according to figures from the British Bankers' Association.
The cost of hedging against losses on European bank bonds has risen by 63 per cent in the past month, with the rates banks are charging each other to borrow three-month loans in dollars hitting their highest point for nine months.
Robert Baur, chief global economist at Principal Global Investors, told Bloomberg banks are showing "a lack of trust in the system".
"Banks are a little reluctant to lend overnight as they don't know the full extent of what is on the bank balance sheets [of other firms]," he said.
Last month, a Credit Suisse report warned that Barclays has around Â£40 billion ($60.9 billion) worth of exposure to troubled European economies such as Spain and Portugal, while RBS is estimated to have around Â£35 billion worth of exposure, reported the Guardian.
By Tony Aynsley