The chancellor's plans to make changes to the banking system, to protect people's savings in the future, have been supported by UK banks.
Mr Darling says he is looking at a wide package of financial reforms
Angela Knight, chief executive of the British Bankers' Association (BBA) welcomed Alistair Darling's suggestions which he made in the Times newspaper.
The changes would mean an increased guarantee for people's savings of up to £100,000 in the event of a bank crisis.
Ms Knight said the time was right for a range of changes to be considered.
Writing in the Times on Saturday, Mr Darling said the rise in guarantees by the government was a "bullet that needs to be bitten" and would be paid for by a levy on banks.
Mr Darling said he was considering a wide package of financial reforms in the light of the Northern Rock crisis - but that these were still in the early stages of development.
Speaking to BBC News, Ms Knight said: "When you've had the sort of problem we've had with Northern Rock and the difficulties in sort of gripping the issue, what we can't do is just say 'that was a one-off, let's leave it alone'.
"I think it is a one-off but we do need to look at our system and there's some obvious pinch points within the system and many of those have been highlighted in the article and we're working on them within the BBA at the moment."
The Bank of England has called for more protection for customers' savings.
The current system, guaranteeing 100% of the first £2,000 and 90% of the next £31,000, contributed to this month's run on Northern Rock, says the Bank.
It was "logical" for savers with more than £33,000 to rush to take it out, its governor Mervyn King told MPs this week.
Some of the planned changes to banking rules were already in the pipeline before the run on Northern Rock and would be announced when the House of Commons returns next month, Mr Darling said.
According to the Times, he is looking at an American-style system, where savers' money is guaranteed and paid out days after a bank collapses, funded by a levy on banks and other financial institutions.
The chancellor will himself be called before the treasury select committee to explain why the Bank of England and financial authorities failed to foresee the recent crisis.
John McFall, chairman of the committee, told BBC News 24 the current compensation scheme was "inadequate," and that the chancellor's proposals were a step in the right direction.
Shadow chancellor George Osborne promised the Conservatives would help the government to push through any changes that were needed.
He told BBC News: "We are happy to work with the government to put in place new financial compensation arrangements and speed their passage through Parliament."
However, Liberal Democrat treasury spokesman Vince Cable said the proposals did not go far enough.
He said: "The chancellor's plans to guarantee bank deposits up to £100,000 is a necessary sticking plaster to stop bleeding from the banking system.
"But there are much deeper wounds that need properly addressing as soon as possible."
Mr Cable agreed that the money should come from the banks rather than taxpayers.
The whole lending system needed to be looked into, he said, blaming the government for showing a "complete neglect" of household debt problems.
Mr Darling described the international credit crunch caused by the collapse of the US sub-prime mortgage lending market and the resulting problems at Northern Rock as a "major upset".
"What's happened in America, and what's now affecting countries all over the world is a major shock to the system.
"Its effects have been felt here, in the Far East, and we have to deal with it," he told the Times.
But he was optimistic about the future of the UK housing market.
Queues were seen at Northern Rock branches across the country
Last week the Bank of England was forced to give emergency financial support to the Northern Rock.
The Newcastle-based firm was the highest-profile UK victim of the global credit crunch, triggered by the sub-prime mortgage crisis in the US.
The crisis resulted in a rush of customers at Northern Rock branches across the country queuing to withdraw savings, fearful that the business could collapse.
The bank has refused to comment on claims in the Financial Times that it has borrowed £3bn from the Bank of England in the past week.