Only a quarter of the people expected to lose out as a result of the abolition of the 10p income tax band will get help from Gordon Brown’s compensation package if it contains the options indicated by ministers, a leading independent think-tank has found.

As Alistair Darling appeared to have reassured Labour MPs finally that low-paid workers would have their compensation backdated to the start of this financial year, the Social Market Foundation’s figures highlighted the limitations of the rescue efforts.

In a report rushed out after Mr Darling’s climbdown on Wednesday, the SMF said that the Chancellor’s proposals, which are aimed at helping the worst-hit losers, were constrained because of a shortage of cash and the difficulty of targeting losers. Ministers have suggested privately that the package will cost less than £1 billion.

Mr Darling has said that he wants to compensate pensioners aged 60-64, low-paid workers without children, and other younger workers. The SMF says that if he does that, as expected, using winter fuel payments, the national minimum wage and working tax credits it will cost from £500 million to £1 billion, and help fewer than a quarter of the worst-hit.

The report illustrates the difficulties facing the Government in trying to come up with a package that MPs will be happy with. After confusion overnight about the extent to which the face-saving deal would be backdated, the Chancellor told MPs in the Commons yesterday that the average losses suffered this year by low-paid workers as a result of the tax changes would be “offset”.

He omitted to mention “backdating” the payments, although his officials were less reticent and said that the average losses, compensated for in tax credits, would cover April 1 to March 31 this year. The effect would be backdating, they said.

The row, which Gordon Brown thought he had defused, threatened to erupt again after Yvette Cooper, the Treasury Chief Secretary, suggested in a late-night television interview that only the compensation for pensioners under 65 would be backdated.

Frank Field, who led the threatened Labour backbench rebellion, accused her of being “badly briefed”.

In an interview with the BBC Radio 4 Today programme, yesterday morning he said that he had an assurance from Mr Brown that the entire package would be backdated to April 1 — the start of the current tax year.

“This is an agreement that the Prime Minister actually put his stamp on,” he said. “There will be a compensation package, it will be backdated.”

Tory leader David Cameron said that the Government was in a “complete shambles” on the issue. “Even when it comes to making a U-turn, this Government is incompetent. With this Prime Minister and with this Chancellor you have always got to check the small print,” he said.

Concern continued to surface over the way Mr Brown had handled the issue. Ian Gibson, the Norwich North MP, said he had six months to show that he was in touch with public concerns. “He has got to listen to who is suffering. All this stuff about 10p makes it sound as if he doesn’t really listen,” he told The World at One.

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