In an unprecendented move late on Monday, Alistair Darling, Britain's finance minister, said the Bank of England would guarantee all deposits held by Northern Rock.
"I do recognise that people are concerned, that's why we have put the matter beyond all doubt," Darling said at a news conference after a meeting with Henry Paulson, the US treasury secretary.
Last week Northern Rock shares fell by over 30 per cent after it said it faced severe difficulties raising cash to cover its liabilities amid the ongoing global credit squeeze.
On Tuesday, Financial Services Authority, the UK's financial regulator, said limits on the current safety net for deposits may have contributed to the uncertainty that prompted thousands to withdraw their savings.
Under the current UK arrangement, guaranteed compensation is limited to 31,700 pounds.
However, account holders remained worried.
|Customers began queuing to withdraw to|
withdraw their funds last week [AFP]
About 50 people were waiting for the Northern Rock branch in Kingston-upon-Thames in southwest London before it opened at 8am.
"I don't know what we will do with the money yet, but I don't trust what the government says," said Doria Watson.
"We were here yesterday but were told we had no chance of getting in, so we are back today and will wait as long as we have to."
Joyce Hutton, who was queuing for a second day, said: "What the government has said gives us more hope, but there is still doubt and I am not taking any chances."
Customers at Northern Rock, which provides one in 13 British home loans, are estimated to have withdrawn at least two billion pounds ($4bn) since Friday.
Attempts by Adam Applegarth, Northern Rock's chief executive, to allay customer fears and unease across the sector had done little before Tuesday to reduce panic among many account holders.
There have been mounting concerns that Northern Rock's problems would spread across the industry, and the government's move on Monday helped shares rebound across the sector .
The bank is the first major British financial institution to be hit severely by the global credit crunch sparked last month by a crisis in the US subprime, or high-risk, mortgage sector.