After three of the four leadership candidates disowned her proposal, Ms Harman was forced into a change of policy and said the party will abstain on the second-reading vote of the Welfare Reform and Work Bill next week.
The retreat by Ms Harman will allow a new leader to come up with a completely different policy for the party to unite around once he or she is in place in September.
Ms Harman will also say that the party will campaign over the summer against plans to scrap child poverty targets, other cuts in tax credits planned for next year before the new living wage comes in, changes to employment support allowance which will hit disabled people and a reduction in the student maintenance grant.
The acting Labour leader put the proposal to an angry party meeting of MPs last night as a compromise.
A source close to Ms Harman said: “She is very clear we need to be a responsible opposition and not oppose for opposing’s sake.
“If we oppose everything then people will not take any notice of us on the things we really need to oppose.”
He added: “It is self-evident though that after September, a new party will be able to have a different policy.”
However, the SNP called on Labour to oppose the bill next week and “stand up to Tory cuts”.
SNP welfare spokesperson Dr Eilidh Whiteford MP said: “Labour may not be willing to stand up to the Tories and oppose these cuts which leave 13 million families worse off – but the SNP will provide the real opposition in this parliament.
“In Scotland tax credits are overwhelmingly paid to working people. And in Scotland 95 per cent of tax credits are paid to families with children. So we should make no mistake about where the cuts are targeted.
“And the idea that the changes to the minimum wage will fill the gap is simply ludicrous.”