Labour has promised compensation to more than three million women who lost out on years of state pension payments when their retirement age was raised, if it wins the general election.
Shadow chancellor John McDonnell said the pledge would settle a “debt of honour” to women born in the 1950s.
Those expecting to retire at 60 were told they would have to wait years longer when changes to the state pension age were accelerated in 2010.
Labour said its promise may cost £58bn.
The costing was not included in the party’s manifesto, published earlier this week.
Questioned by Sophy Ridge on Sky News, Mr McDonnell said it would be funded by a “very special arrangement, a contingency, in the same way government in the past has dealt with matters in the past like this”.
The retirement age for women rose to 65 in 2018, in line with men, and will go up to 66 by 2020, and to 67 by 2028.
It follows a campaign by so-called Waspi women – the Women Against State Pension Inequality – who had argued they were not given enough time to prepare for the changes.
Another group of campaigners known as Backto60 recently lost a significant legal battle against the government over its handling of the issue.
Labour said it would make individual payments of an average of £15,380 to the 3.7 million women it claims were affected, with some payouts as high as £31,300.
Mr McDonnell said the compensation, which the party says could cost £58bn over five years, would make right a “historical wrong”.
He told Sophy Ridge that the women affected “had done everything that had been asked” of them during their working lives and many had been “forced into penury” through no fault of their own.
“This is a historic injustice and we have to address it. Some of these women are older and may not be with us if we don’t act quickly.”
He said Labour was working on the assumption that the women ultimately won their legal fight for financial redress against the government.
“It is expensive but it is an entitlement, it is not a benefit…The scale of this injustice is enormous”.
Asked why the cost of the policy was not included in Labour’s manifesto, he said it was being treated differently from other financial commitments, likening it to compensation the government had to pay to mesothelioma victims after losing a long-running legal battle last year.
Shadow Education Secretary Angela Rayner said justice for those affected was a “price worth paying”.
“People should have confidence in their government that they are not going to steal their pension,” she told the BBC’s Andrew Marr show. “It fundamentally undermines the contract between the state and its people.”
Labour has already promised to freeze the state pension age at 66 for the foreseeable future, a move which would cost billions of pounds more than most recent government plans to raise the age for men and women to 68 by 2039.s
How did we get here?
From 1948 for more than 60 years men received their state pension at 65 and women at the age of 60.
But over the years it was argued that the difference was unfair, as women had a longer life expectancy than men.
So under the 1995 Pensions Act a timetable was drawn up to equalise the age at which men and women could draw their state pension.
The plan was to raise the qualifying age for women to 65 and to phase in that change from 2010 to 2020.
But the coalition government of 2010 decided to accelerate that timetable, arguing that the state pension was becoming unaffordable.
Under the 2011 Pensions Act the new qualifying age of 65 for women was bought forward to 2018 – affecting millions of women.
While some of them had time to adapt to a longer working life, for others the change came as a shock.
Labour’s pledge comes as a contrast to the Conservative Party’s outlook on the Waspi campaign.
Boris Johnson was challenged by one of the women affected in Friday’s BBC Question Time leaders’ special.
The prime minister said: “I do sympathise deeply with the Waspi women… but it is very expensive to come up with the solution you want.”
“I cannot promise I can magic up that money for you,” he added.
By Katie Prescott, BBC News business correspondent
Labour describes the issue of the change in state pension for women as a “historical debt of honour” that the country needs to pay for.
Or in its words “the state will be expected to find the money, just as it would do if the government lost a court case, rather than a policy decision”.
Critics say this means the party has no idea where the money is supposed to come from.
But there is much sympathy for the women caught up in the change to the state pension age, many of whom have led a grassroots legal battle against the government on the issue for years.
Even while ruling against them, the judges in the case acknowledged “the court was saddened by the stories contained in the claimants’ evidence”.
And this clear support from Labour – lining up squarely against the government’s stance on the issue – could be very popular.