Chancellor Alistair Darling stepped in to restore calm to the situation.
In a statement he said: "As I have said on many occasions over the past few days, people are able to get their money out if that is what they want to do."
"I can announce today that the following discussions with the Governor and the Chairman of the FSA, should it be necessary, we, with the Bank of England, would put in place the arrangements that would guarantee all the existing deposits in Northern Rock during the current instability in the financial markets."
"This means that people can continue to take their money out of Northern Rock. But if they choose to leave their money in Northern Rock, it will be guaranteed safe and secure," he said.
Mass queues of customers looking to withdraw their money have been growing outside the bank since it was announced that the Bank of England may provide emergency funding.