Lord Turner made the comments in a roundtable discussion
The boss of UK watchdog the Financial Services Authority (FSA) says he would be happy to consider a tax on banks to prevent excessive bonus payments.
FSA chairman Lord Turner also told Prospect magazine that the financial services sector had "grown beyond a socially reasonable size".
The FSA said he was "not setting out any new policy" and the government said taxation was a matter for the Treasury.
The FSA's regulations on bonuses have been criticised for being too weak.
They were announced on 12 August, five days after Lord Turner took part in Prospect's roundtable discussion.
The new rules, which will come into effect in January, will ensure bank bonuses are not guaranteed for more than a year, and that senior employees have their bonuses spread over at least three years.
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"I think this illustrates Lord Turner's frustration at the 'back to business as usual' mode of the financial services industry," said John McFall, chairman of the House of Commons Treasury Committee.
"In effect he's saying 'Why should the financial services industry be alone in requiring this model of bonuses?' and that it is not in line with the rest of the economy."
But some analysts have suggested there may be political reasons for Lord Turner to be sounding tough on the City.
"[The comments] may be a ploy to persuade Mr Osborne and the Conservatives that, were they to be elected, they should retain the FSA rather than pass the baton for regulation to the Bank of England, which is one of the shadow cabinet's proposals," James Bevan from CCLA Investment Management told the BBC.
Lord Turner said that a tax on financial transactions in the City would cut banks' profits, and thereby reduce the funds available for bonuses.
He said it could be "a nice sensible revenue source for funding global public goods".
But he conceded that "the problem is that getting global agreement will be very difficult".
G20 leaders have been discussing bonuses and said in April that they would clamp down on excessive pay.
French banks have recently agreed to a new set of rules. These mean there will be penalties for traders who lose money, as well as rewards for success.
French President Nicolas Sarkozy has said he will press for tougher controls on bankers' bonuses at the next G20 summit in the US city of Pittsburgh in September.
Chancellor Alistair Darling will be raising the issue at next week's summit of G20 finance ministers.
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