Analysis By Jennifer Clarke Personal finance reporter, BBC News

Alistair Darling faces his biggest challenge since becoming chancellor

As shares in the beleaguered Northern Rock continue to fall, Alistair Darling faces the biggest challenge of his career.

Under fierce fire from opposition MPs, the chancellor has defended his handling of the crisis.

He insisted the emergency loans granted by the Bank of England, and the government's decision to guarantee savers' money on deposit with Northern Rock, had stopped the problems spreading to the rest of the banking sector.

But it will not be easy for the government to extricate itself from a growing political and economic quagmire.

Selling Northern Rock as a going concern is seen as the best option for government, staff and shareholders.

It would avoid the acute embarrassment of a bank collapse.

Depositors' money would be safe and borrowers would see little change.

It may also offer the greatest protection to jobs and the bank's branch infrastructure.

Shareholders may get little benefit in the short term, but could gain in the future from a revitalised company.

But this route is not without complications.

It is thought around 10 companies have expressed an interest in Northern Rock.

Front-runners include Richard Branson's Virgin Group, a consortium headed by former Abbey National chief Luqman Arnold, and the private equity firm JC Flowers.

It is not clear how much money is on the table under any of the bids. But on Monday Northern Rock said the proposals received so far were "materially below" the bank's closing share price on Friday, which valued the bank at �558mn.

Shares have fallen substantially since then.

And there's the tricky question of those Bank of England loans.

The government has said continuing financial support may not be legal under European law.

But it is not certain that any bidder will be prepared to buy Northern Rock without the loans continuing for some time.

Under this option, Northern Rock could be broken up and its various assets sold off.

The problem is we don't know how much its assets are actually worth.

A leaked memo which had apparently been circulated to possible bidders seemed to indicate that savers may have withdrawn as much as �10.5bn from the bank since the summer.

On Monday the chancellor said that Northern Rock's mortgage book remains sound.

But if its borrowers are paying the bank less interest than it is paying the Bank of England to fund their loans, it is hardly an attractive prospect.

BBC Business Editor Robert Peston says leading bidders Virgin Money and JC Flowers both estimate that Northern Rock requires an injection of �1bn of new capital, suggesting the assets may not be as valuable as previously thought.

And the government will not relish the prospect of Northern Rock's branch network or call centre being sold off, given the likely impact on jobs in the North East.

This is nobody's favoured option.

It means that the firm is essentially bankrupt and will be wound up.

Under this route, an accountancy firm would take over the company, realise as much of the remaining assets as possible, and manage the bank's mortgage book.

It would be enormously embarrassing for the government if the first run on a UK bank in more than a century led to its actual disintegration.

Again it is not clear how much the assets would be worth.

But unlike a voluntary break-up, this is a forced sale and the administrator might have to sell at even lower prices.

And shareholders - including 150,000 odd retail investors who got their shares when the former building society floated in 1997 - would probably get almost nothing, as they are at the bottom of the list of creditors.

Another problem is that under current UK law it could take some time before depositors could get their money back.

It is likely the government would come under substantial pressure to fulfil its �16bn promise to guarantee all savers' deposits immediately.

That could seriously complicate the situation.

And as before the government would not welcome the likely job losses or branch closures.

This is the option favoured by the Lib Dems and various other commentators. They believe it is the only way the government can protect the billions of pounds already advanced.

The Treasury would take control of the bank and manage the winding down of the business.

It is not clear how such a move might sit with the EU competition authorities if the government was seen to use public money to prop up a company which continued to trade.

And this option would run entirely contrary to the government's light-touch approach to the regulation of the private sector.