Sir David, a former executive director of the Bank of England and former chairman of the Securities and Investments Board, he is now a senior adviser at Morgan Stanley International.
His preliminary conclusions are not due until the autumn and final recommendations by the end of 2009.
The timescale fuelled complaints from opposition parties that the Treasury response was too slow.
Shadow chancellor George Osborne said it was "inadequate" and the review would come "far too late" to do anything about this year's bonuses.
Lib Dem treasury spokesman Vince Cable said: "Instead of dealing decisively with the problem, as President Obama, the Swiss and others have done, the government is clearly playing for time in order to avoid doing anything to upset the bankers."
The independent investigation will also look at the pay and bonuses of top executives in the industry.
"The chancellor feels he has the right to limit bonuses and set conditions on pay at any bank propped up by us, by taxpayers, which broadly includes all British banks, since they've all received exceptional loans and guarantees from taxpayers over the past few months," said BBC business editor Robert Peston.
Banks were said to be looking to pay a fraction of last year's bonuses.
But the scale of the reported pay-out at RBS has caused an outcry, after the company had to be taken into 68% public ownership at a cost of £20bn in taxpayer money.
Alistair Darling: 'We've got to make sure success is rewarded not failure'
RBS has experienced a year of turmoil, and has already flagged up that it will post a huge loss for the past 12 months.
In January RBS said it was heading for a record loss, and expected to report a deficit before write-downs of between £7bn and £8bn for 2008.
Mr Darling told BBC One's Andrew Marr Show that "no figure on bonuses has been agreed on" but said he had told RBS no-one associated with the losses should be rewarded.
"I have spoken to the chief executive of RBS, and made it quite clear - and he agrees - that no-one associated with these huge losses should be allowed to walk away with large cash bonuses," Mr Darling told the programme.
But he added: "Obviously there are contractual problems with some staff. And... if you look at your average teller, they're not terribly well paid, and no-one would quarrel with making sure they are properly rewarded."
You don't need a review to answer the simple question: should senior bankers receive bonuses? The answer is no
Liberal Democrat leader Nick Clegg
He said that in the past a bonus was a reward for hard work or extra effort, but was now seen as a right by bankers.
He added that the bank wanted "to make sure they cut down these payments to the absolute minimum they have to."
"They have to understand that these banks would not be here but for the British taxpayers, therefore they have to show the degree of restraint that people would expect."
The shadow chancellor told the Andrew Marr Show: "The party is over for the banks.
"For senior management, cash bonuses at a time like this for people who have been involved in the higher echelons of a bank is simply unacceptable."
George Osborne on 'unacceptable' cash bonuses
Mr Osborne added that there had to be a new economic model, and that "the bankers and indeed the government have to understand you can't just reflate the balloon that burst".
Referring to the Treasury inquiry, he also questioned the need for "yet another review".
Liberal Democrat party leader Nick Clegg told the BBC's Politics Show: "You don't need a review to answer the simple question: should senior bankers receive bonuses? The answer is no."
RBS confirmed it was talking to the government about bonuses but declined to comment on any specific numbers, adding that it had contractual obligations to many executives but was trying to do the right thing at the same time.
The bank has said that any bonuses will be dramatically reduced and there will be "no reward for failure in those bits of its business where the losses were concentrated".
Meanwhile, former deputy prime minister John Prescott, who runs an online grassroots banking campaign, said: "We are all [RBS] shareholders now and the shareholders demand you give up the bonus."
One of the key issues that will be examined in the Treasury review is the extent to which financial incentives encourage bankers to take risks.
Looking at very detailed as well as general changes to remuneration structures is something that the banks are already doing
Angela Knight British Bankers' Association
Mr Darling said that it would be wrong to reward people whose excessive risk-taking brought the banks down.
Angela Knight, chief executive of the British Bankers' Association, said the size of bonuses was likely to come down in future.
"They have seemed very high," she said. "What I will say is that I don't think you'll see those again."
She added: "Looking at very detailed as well as general changes to remuneration structures is something that the banks are already doing."
Last week US President Barack Obama announced a $500,000 (£355,000) limit on executive pay at US firms that needed substantial fresh government aid.
The move follows widespread public anger over the levels of pay on Wall Street, but is not expected to be applied retrospectively.
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