Worried savers have continued to flock to some Northern Rock bank branches to withdraw their savings, following similar scenes over the weekend.
Bank boss Adam Applegarth said people could withdraw money and that it was "business as usual", while Chancellor Alistair Darling appealed for calm.
About £2bn has been withdrawn since Thursday, when the bank applied to the Bank of England for emergency funds.
Northern Rock shares were 40% down at one point and ended 35.4% lower.
Shares in other mortgage banks also suffered, with Alliance & Leicester slumping in late trading to finish 31.3% lower. Bradford & Bingley shares were also down, losing 15.4%.
NORTHERN ROCK CRISIS
Bank needed £1.6bn from Bank of England to stay afloat
Had been financing lending by borrowing on credit markets
Fears about exposure to bad loans in the US dried up credit
US economy expected to slow as bad loans hit housing market
Uncertain how much exposure other banks have to bad debt
In London, Northern Rock's shares, which had lost 32% on Friday, fell from 438 pence to 282.75 pence.
'Bank of England backing'
Mr Darling had told the BBC's Radio 4 Today programme that the money of Northern Rock depositors was safe.
"If people want to get their money out of Northern Rock bank, they can do it. The money is there and it is backed by the Bank of England so they can get it," he said.
Northern Rock says it has not used any of the Bank facility for funds offered to it.
The chancellor and Prime Minister Gordon Brown will meet US Treasury Secretary Hank Paulson to discuss the growing turmoil in world financial markets later on Monday.
Northern Rock branches had opened at 0800 BST on Monday - an hour earlier than usual.
Lindsay Topping, 59, from Cliftonwood in Bristol, who has tens of thousands of pounds in her Northern Rock account, said: "I've got quite a lot of money in there.
"I'm not sure what I'm going to do with it. I'll wait and see what I'm told. It's impossible not to feel a bit panicked after the coverage we've seen over the last few days."
It is understood Northern Rock was almost sold to rival bank Lloyds TSB.
However, the deal fell through because of the difficulty of borrowing money in the current financial climate.
The lower the Northern Rock share falls the easier it would be for a rival to take it over.
Experts at Lehman Brothers said in a statement: "Any interested buyer appears to be in a strong position over price."
Mr Applegarth told the BBC he could not discuss possible takeovers, nor would he confirm the exact amount of cash withdrawn from bank branches since Friday.
Not all Northern Rock branches have seen big queues on Monday. No one at all has been queuing in Belfast, Bournemouth, or Swindon.
On Friday, Northern Rock shares fell 32% and will be closely watched this week.
As well as extending its opening hours, Northern Rock has also increased bandwidth on its online banking, which has struggled under the volume of people trying to access the website.
The BBC's business editor Robert Peston said the £2bn withdrawn - which represents about 8% of the £24bn deposits it held on Thursday - was actually less than the mortgage lender and officials at the Bank of England and Financial Services Authority had feared.
However it cannot be certain whether much more will be withdrawn in the coming days, especially from holders of Northern Rock's postal accounts - which contain about £10bn.
The City watchdog, the Financial Services Authority (FSA), has backed comments from the Treasury, saying it is confident Northern Rock is solvent and savers could continue to deposit and withdraw funds.
The BBC has learned that two banks were very interested in acquiring the beleaguered firm. However, they were concerned about doing such a big deal amid turmoil in money markets and when it was difficult and expensive to raise money from other banks and financial institutions.
Mr Darling said the emergency lending facility offered to Northern Rock would be transferred to any new owner.
However once the facility expires - and the Bank will not make the expiry date public - there is no guarantee it would be extended for the new owner.
"Most bidding banks will remain nervous about taking on a balance sheet of Northern Rock's size with the risk hanging over it of needing to refinance a large chunk of loans from the Bank of England at short notice in markets which may remain frozen," Robert Peston said.
Northern Rock's realisation that selling the bank had become impossible in current market conditions, persuaded the board to approach the Bank of England and ask for access to emergency loans, he added.
"Plainly, a takeover would have been a less humiliating option. But it just couldn't be done."
Northern Rock has struggled to raise money to finance its lending ever since money markets seized up over the summer.
Unlike most banks, which get their money from customers making deposits into savings accounts, Northern Rock is built around its mortgage business.
It raises most of the money which it provides for mortgages by borrowing from banks and other financial institutions.
WHAT'S HAPPENING AT NORTHERN ROCK?
Mortgage lending Northern Rock lends a large amount for mortgages, and finances this with money from banks and savers
Savings Northern Rock receives a relatively small amount of money from savers
Money markets Have stopped lending money to Northern Rock due to the crisis in the US sub-prime mortgage market
Bank of England Steps into the breach to give Northern Rock an emergency loan
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