Labour backbencher John Mann told the BBC he believed it would save the taxpayer £20m a year and amounted to "a cut" for MPs.
Ms Harman said ministers living in "grace-and-favour" homes would not be able to claim the new allowance.
Nor would MPs with constituencies "within reasonable distance of Westminster" who would instead be entitled to the supplement currently claimed by inner London MPs, worth up to £7,500 a year.
The statement was inadvertently revealed early to the press when Communities Secretary Hazel Blears held the document in her hand in Downing Street in full view of press photographers.
The Committee on Standards in Public Life, headed by Sir Christopher, is due to publish a review of pay and expenses by the end of the year.
BBC political correspondent Reeta Chakrabarti said the announcement had come as a big surprise to many in Westminster, the day before the Budget, as three weeks ago Mr Brown appeared to rule out any changes before that review was complete.
But Mr Brown, who has seen several ministers embarrassed by revelations about their expenses, said MPs had to "act urgently" to restore public confidence.
In a video statement on the Downing Street website, he added: "The issue of expenses is casting a cloud over the whole of Parliament.
"So members of Parliament need to have the humility to recognise that the country has lost confidence in the current system."
David Cameron: 'A welcome U-turn'
Sir Christopher told BBC Radio 4's PM programme the prime minister had assured him the plans were merely "interim recommendations".
"If public confidence is going to be restored, what is required is... a proper, independent, fundamental look at the issue and at all the issues not just those identified in the statement," he said.
"I have warned on numerous occasions that this is not something that can be solved by a quick fix."
Lib Dem MP Nick Harvey, who sat on the committee which last year reviewed MPs' expenses, told the BBC Mr Brown should have waited for the review rather than revealing proposals "for some sort of political advantage the day before the budget".
He said a flat daily rate that covered MPs' existing rental agreements was bound to be considered "quite high" and people might think paying out a lump sum was "more opaque and secretive" than filing claims for rent or mortgage payments.
Mr Brown has offered to meet Conservative leader David Cameron and Lib Dem leader Nick Clegg in the next week to discuss the proposals.
Mr Cameron said the announcement was "a significant and very welcome U-turn" from Mr Brown and said he was in favour of moves to "cut the cost of politics".
He told the BBC: "This is progress but I do worry about this idea of paying MPs a per day amount to turn up and do their jobs. I think that is open to exploitation, there will be loopholes and problems - I will go to this meeting and try to help sort them out."
Lib Dem leader Nick Clegg was also concerned about the proposals for a daily allowance and said every pound claimed should be justified to the taxpayer.
I don't think bringing the Brussels gravy train to Westminster is the answer to our problems
Mr Clegg, a former MEP, told BBC Radio 4's World at One: "This is what they do in the European Parliament and I don't think bringing the Brussels gravy train to Westminster is the answer to our problems."
Calls to reform second home allowances have increased, with revelations about several MPs' use of the money.
Home Secretary Jacqui Smith and work minister Tony McNulty are both being investigated over their claims although both say they acted within the rules.
The furore over expenses began last year when it emerged Conservative MP Derek Conway had claimed thousands of pounds for employing his two sons as researchers, although they had done far less work than reported by him.
MPs voted last July to keep second home expenses and rejected proposals for a tougher auditing regime.
Mr Brown did not vote, while 33 government ministers backed keeping the allowances.
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