Writing in his blog Robert Peston said: "The advantage of taxing these bonuses are first that they are likely to be pretty popular with more-or-less everyone apart from the bankers, if opinion polls are to be believed.
"But also, taxing bankers rather than banks would not weaken the banks themselves, at a time when they need to accumulate capital."
He added: "But there might be almost no revenue from it for the Exchequer - even less than the few hundred million pounds expected by the Treasury."
And one tax expert, Mike Warburton of accountants Grant Thornton, said there were potential problems in identifying who would have to pay any new tax.
"How do you define bankers? Would it include people working at Goldman Sachs, who didn't receive a government bail-out?"
He added: "There is any number of ways I'm sure that able minds will find to get around any sort of selective tax that's brought in bonuses."
State-owned Royal Bank of Scotland reportedly wants to pay a total of £1.5bn in bonuses to investment banking staff, and the board has threatened to quit if the government blocks the move.
RBS' financial statements show that one reason why its investment bank has seen a surge in profits has been due to a big change in the way the group presents its accounts
Speaking on BBC One's Andrew Marr Show on Sunday, Mr Darling played down speculation about a windfall tax.
He said the government had a "veto" over bonuses at RBS but said the bank had "not come to us with any proposals at all at the moment because they don't yet know what the end of year position will be".
But he stressed: "These bonuses have to be reasonable and they have to be responsible and I think everyone has to accept that."
He added: "We are not going to be held to ransom by people who believe you can pay extraordinarily high bonuses without regard to what's going on."
But he also acknowledged that there had to be "sufficient incentives" to ensure RBS got back onto a "proper footing" and off the government's books.
'Gifted vast profits'
Robert Peston said if a windfall tax was imposed it would not just apply to UK banks such as Barclays, HSBC and Royal Bank of Scotland, but also to the British arms of overseas firms, such as Goldman Sachs, JP Morgan and Deutsche Bank.
When the banks start making profits again they should start paying taxes again
"The fact is that we have gifted vast profits to the banks as a result of our actions," our correspondent quotes one minister as saying.
"If they were using those profits simply to strengthen themselves that would be okay. But what we can't accept, and what society can't accept, is that they are using those profits to pay enormous bonuses".
Our correspondent also said taxing the bankers may not be cost-free for the UK.
"It would not be great for the economic prospects of the UK if wealth-creating bankers and financial institutions emigrated to rival financial centres - for fear that the UK is becoming irredeemably hostile to them," he said.
Mark Tilden, a consultant at CRAI, carries out research on how taxation influences company decisions, said: "I think everyone has always been a bit offended by bonuses of £5m or £10m... but the fact is these people are mobile and they will leave."
In the longer term, the prime minister and chancellor want a permanent levy on bank transactions, a so-called Tobin tax.
Shadow chancellor George Osborne, for the Conservatives, said he "wouldn't rule out" a windfall tax on bonuses, but would prefer reforms to ensure banks pay tax on future profits.
Liberal Democrat Treasury spokesman Vince Cable told the BBC "a special tax on the banks' profits" should last as long as the "banks continue to depend on taxpayer guarantees".
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