A Barclays spokesman told Reuters the bank had "categorically not" requested any funds from the UK government.
"We have categorically not requested capital from the government," Barclays spokesman Alistair Smith said, declining to comment on whether the bank had been involved in talks with the government on a potential recapitalisation.
RBS said much the same, according to Reuters, while a Lloyds TSB spokeswoman told CNBC "we haven't got any comment" on the report.
The request was made at a meeting with Darling last night, which was also attended by Bank of England Governor Mervyn King and Adair Turner, chairman of the Financial Services Authority, the BBC said.
The three banks estimate that they may need around 15 billion pounds of new capital each, with 7.5 billion pounds paid up front and a further 7.5 billion guaranteed by the Treasury that would be delivered if it became necessary, the report said.
The UK Treasury declined to comment, but said it would do whatever was necessary to maintain stability.
"As the Chancellor (of the Exchequer Alistair Darling) said yesterday, we will do whatever it takes to maintain stability and support a well-functioning banking system," a spokesman said.
A spokesman for Prime Minister Gordon Brown's office said he would not speculate on possible policy options. Britain's banking regulator, the FSA, declined to comment.
"I think what this signals to me is that this isn't a situation where banks can muddle through. They're going to have to be recapitalised and they're going to be heavily dependent on government and the authorities for sources of funding," said Simon Pryke, head of global research at Newton Asset Management.
An industry source told Reuters the next round of talks will focus on what form of equity the government would receive in return for providing banks with any injection of taxpayer's money.
"That's what they will be working on over the next couple of days," the source said.
The cost of insuring the debt of the three banks fell sharply on the reports of a possible capital injection.
Five-year senior credit default swaps on RBS were about 30 basis points tighter at 270 basis points and about 20 basis points tighter at 230 basis points on Barclays, a trader said. That means investors have to pay 270,OOO and 230,000 euros to insure 10 million euros of the respective banks' debt against default.
"It's more of an equity story, as it look like shares will be diluted, while a capital increase is credit positive which explains how the CDS has reacted," a credit trader said.
Meanwhile European Union finance ministers are meeting in Brussels to discuss options on measures to restore confidence in the banking sector, but analysts say that the most likely outcome will be an agreement on guaranteeing private savings, without other major decisions.
Interbank money markets -- blocked for months by banks' refusal to lend to each other -- remained logjammed, with the cost of borrowing euros for three-month staying as high as 5.38 percent on Reuters system.
The FTSEurofirst 300 index fell to four-year lows on Tuesday. MSCI main world equity index fell 0.5 percent, having lost more than 9 percent this month alone.
Brown and Darling will hold talks on the financial crisis with the governor of the Bank of England, Mervyn King, later on Tuesday, a spokesman said.
-- Reuters contributed to this report