Labour MP Frank Field has vowed to continue to fight the government if low earners affected by the 10p tax band's axing are not suitably compensated.
The MP, who has led a backbench revolt against the changes, said the PM had agreed compensation would cover average losses and be backdated to 1 April.
But Mr Field told MPs they could "take this measure again in our own hands" at a later stage if not satisfied.
MPs have passed the Finance Bill clause implementing the tax changes.
It was passed by 304 votes to 262 late on Monday after a Conservative amendment to the bill, which could have restored the 10p tax rate in 2009, was defeated.
Ministers had seen off a potential backbench revolt by pledging concessions last week.
Financial secretary to the Treasury, Jane Kennedy, told MPs the government was looking to help households on a low income "in the next few days and weeks".
But she refused to be drawn on the issue of backdating the compensation, insisting the package was still being worked on.
However, Mr Field stressed that he understood from Gordon Brown that whenever the elements of the package were announced, they would be backdated.
He told Ms Kennedy: "When you report back on this debate, I'm sure you will report that this side of the House attaches huge importance that all groups will be compensated back to April 1."
The Conservatives, Lib Dems and some Labour MPs say they want to know exactly what is being offered.
The Conservatives argued that the government's plans were so hazy their amendment was needed to ensure ministers delivered.
The amendment would have required the 10p rate to be restored on 5 January 2009 if the government failed to give the House of Commons a debate and vote on its compensation package for people who lost out.
Mr Field last week withdrew his own amendment to the Finance Bill, calling for a compensation package, after ministers pledged to offer concessions to some low earners and pensioners.
But he told MPs on Monday: "We have the right to take this measure back again in our own hands when the Budget comes back again at report stage."
He said Mr Brown and Chancellor Alistair Darling had agreed the compensation package would be "as comprehensive as possible" and he suggested it could be delivered through tax credits or the revenue system.
The abolition of the lowest rate of income tax came into effect this month, alongside a reduction in the basic rate of income tax from 22p to 20p and increases in child benefit and tax credits.
Last week the government said it would outline a compensation package for pensioners aged 60 to 64 and low earners by this autumn's pre-Budget report, following concerns that 5.3 million of the UK's lowest earners were losing money.
Conservative leader David Cameron told the BBC the prime minister had not been clear about the form the planned compensation would take.
The Liberal Democrats' Treasury spokesman Vincent Cable said he thought most of the 5.3 million would still lose out and said the "supposed concessions" would "not make a blind bit of difference to the millions who are already feeling the pinch from Gordon Brown's tax grab".
Mr Straw told BBC Radio 5 Live on Monday that the full effects of scrapping the 10p tax rate had not been anticipated, saying: "Sometimes, even with the best brains available to government, there are inadvertent consequences of changes and we put our hands up to that."
He told one caller who had lost money: "I am sorry that you have been placed in this position and it shouldn't have happened."
Meanwhile Mr Brown insisted more people were better-off after the tax changes in the 2007 Budget, which he said had helped pensioners and families with children.
Mr Brown acknowledged that "there were two issues arising from that Budget that needed more attention and that's what we've done".
However, he added: "I think the background to the Budget that people will probably remember most years from now is that we've reduced the basic rate of income tax from 22 to 20 pence, and we've done a lot more to help family poverty be eased."
The Finance Bill debate will continue on Tuesday.