Customers of the troubled Northern Rock bank have complained of problems accessing their online savings accounts because of massive demand.
Customers have been withdrawing money despite appeals for calm
Savers have rushed to take money out of Northern Rock, amid concerns over its emergency Bank of England loan.
Its branches saw long queues of worried customers on Friday and Saturday.
Meanwhile, BBC business editor Robert Peston says a number of banks are considering a takeover of the bank - but no deal looks likely soon.
Northern Rock insists that the problems with its website are "entirely logistical" and "in no way related to the bank's solvency".
According to online customers the only way they can get to their money is via the internet, due to the terms of their accounts. But demand is so high that many cannot access the site.
"For us online savers they appear to have taken no account of the problems with their website," Paul Hancock from west Sussex told BBC Radio Five Live.
"Their chief executive has said all the time that it's business as normal but with their website being down it's been far from normal for us online savers."
Martin Lass, from Pinner in Middlesex, said he'd recently transferred money into Northern Rock because their online systems were usually very good.
"I'm worried about what the outcome is going to be," he said. "Whether they've got the liquidity to meet all the panic demands of people like myself trying to get to the accounts and get their money to somewhere they know is safe"
Investment bank Merrill Lynch was appointed in the summer to sound out possible buyers, with interest thought to have come from overseas, says the BBC's Robert Peston.
But he said that given how difficult and expensive it is to borrow from the money markets and banks, no firm was keen to pay for Northern Rock's assets of about £113bn.
The emergency lending facility granted to Northern Rock by the Bank of England would also have to be removed if there were a takeover.
"If it didn't do that, the Bank of England could be accused of subsidising the sale of Northern Rock and propping up the value of Northern Rock's shares and bonds, which is the last thing it wants to do," he said.
Northern Rock has struggled since money markets seized up over the summer. The bank is not short of assets, but they are tied up in loans to home owners. Because of the global credit crunch it has found it difficult to borrow the cash to run its day-to-day operations.
Despite reassurances over the safety of their savings, customers have taken out well over £1bn in the last few days. Northern Rock has not confirmed how much money has been withdrawn from branch savings accounts.
Chancellor Alistair Darling and City watchdog the Financial Services Authority (FSA) have tried to reassure customers that the bank was still functioning.
The bank says difficulties with the bank's website "are in no way related to the bank's solvency or its underlying ability to deliver funds to savers who wish to withdraw".
Northern Rock spokesman Brian Giles said the website was running slowly owing to a high number of customers, and insisted: "There is no gate blocking anyone from accessing their account."