The Northern Rock has been seeking to re-assure investors, after the BBC revealed it had sought emergency help from the Bank of England.
The Northern Rock has now secured a very large loan for itself
Northern Rock boss Adam Applegarth said it would still be "business as usual" even if there was a run on the bank.
Speaking during a conference call with investors, he said there had a been a "spike" in activity on its online banking website.
But he said there would be no limits on any cash withdrawals by customers.
Mr Applegarth explained that he had asked for emergency loan facilities from the Bank of England - in effect an authorised overdraft for banks - because the Northern Rock's main source of funds for its mortgages in the financial markets had dried up suddenly in early August.
He blamed the development on the global crisis of confidence in the banking system, which started when US banks making so-called sub-prime loans - to borrowers with poor credit history - ran into trouble.
Since then banks have been very unwilling to lend to each other at all, regardless how safe their investments are.
Mr Applegarth said he had never seen anything like it in 25 years in banking, and did not know when the markets would get back to normal either.
The Northern Rock, the UK's fifth largest mortgage lender as of the end of 2006, will now rein in its mortgage lending activities sharply.
"We have certainly slowed down new lending," said Mr Applegarth.
"We are assuming we will remain hunkered down for the rest of the year," he added.
He explained that the amount of money his bank could borrow from the Bank of England was limited only by the amount of collateral that it could put up. This means the sums could be large, although he revealed that he was not permitted to say exactly how large.
Asked if he or his customers should be worried, Mr Applegarth replied: "Knowing that we have an uncapped facility with the Bank of England, you don't get better than being banked by the Bank of England."
He declined to say what position the Northern Rock might have been in had it not approached the authorities.
Asked about the long term future for the Northern Rock, and whether or not it would remain independent, he said only that the board of directors would review all options in due course.