The UK's financial watchdog, the FSA, is investigating whether rumours have been deliberately spread to undermine the value of bank shares.
The Financial Services Authority issued a warning to traders
It said it would "not tolerate" traders starting "false" rumours about firms to make cash from dealing in their shares.
HBOS, whose shares fell as much as 17% at one stage on Wednesday, denied rumours of funding difficulties.
And the Bank of England also denied that any UK banks were in trouble, and said it had had no meetings with banks.
An HBOS spokesman said: "There has been a series of rumours in the market today. A number of ill-founded and malicious rumours about the UK banking system in the markets.
"These rumours have not a shred of substance whatsoever. They are lies."
And they supported the "decisive action" of the FSA to investigate the alleged market abuse.
"There has been a series of completely unfounded rumours about UK financial institutions in the London market over the last few days, sometimes accompanied by short-selling," the FSA said in a statement.
In short-selling a trader borrows shares, sells them immediately and hopes to repurchase the shares in the future at a lower price.
The trader can then return them to the lender and make a profit on the difference.
Meanwhile, the BBC has learned that the chief executives of major UK banks will be meeting Bank of England governor Mervyn King on Thursday.
The BBC's Business Editor Robert Peston said the banks would like the Bank of England to lend them more money for longer and taking a wider range of assets, especially mortgages, as security.
WHAT IS SHORT-SELLING?
Trader borrows shares, then sells them
Repurchases shares later at a lower price
Trader returns shares to lender
Makes a profit on the difference
"The intention would be to reassure creditors and investors that there is not the faintest chance of any British bank suffering a funding crisis of the sort that did for Northern Rock," our correspondent said.
Northern Rock had to go to the Bank of England for emergency funding in September last year after the credit crisis meant it could not borrow enough money through the financial markets.