Rachel Reeves has pledged to reverse Jeremy Hunt's "regressive" pensions tax break for the top 1% of earners if Labour wins power at the next election.
The Shadow Chancellor said the decision to abolish the £1million pension lifetime allowance - a "gilded giveaway" - was the "wrong priority" and for the "wrong people".
Labour said those with more than £1.4million in their pension pot would be able to pay £150,000 less in tax under the Tory Government's changes.
The Resolution Foundation also branded the move "hugely regressive and wasteful" while being "poor value for money for Britain".
The measure was billed to prevent consultants retiring early from the NHS because the current pensions rules mean it is not worth them carrying on working.
But with the policy helping just 15,000 high earners leaving the workforce early, the think-tank said the cost would be around £80,000 in lost taxation per worker.
Ms Reeves said a Labour government would reinstate the lifetime allowance and create a targeted scheme for doctors rather than allowing a "free-for-all for the wealthy few".
In a statement, the Shadow Chancellor said: “The Budget was a chance for the government to unlock Britain’s promise and potential. But the only surprise was a one billion pound pensions bung for the one per cent, a move that will widen the cost of living chasm.
"At a time when families across the country face rising bills, higher costs and frozen wages, this gilded giveaway is the wrong priority, at the wrong time, for the wrong people."
She added: "That's why a Labour government will reverse this move. We urge the Chancellor and the Conservative government to think again too."
But the Chancellor said scrapping the tax-free cap on the lifetime pensions allowance could help to reduce the £3 billion spent per year on locum and agency staff in the NHS.
He told BBC Breakfast: "We looked at all the different options.
"The other options, if we had a scheme that was just for doctors, it would actually be more aggressive because what we've announced doesn't help the very wealthiest doctors.
"It still keeps in a limit on the amount you can put in tax-free every year, but most importantly, it is something we can introduce in two weeks' time and we can deal with a problem."
In an analysis of the Budget, the Resolution Foundation also warned Brits are in the midst of a "disastrous decade" for living standards.
On Wednesday the OBR forecast that living standards are expected to fall by over 5% over the next two years - the largest decline since records began in the 1950s.
The think-tank added that taxes as a share of GDP are on track to hit a 70-year high of 37.7% by 2027-28 - an almost 5% increase since 2019-20.
Torsten Bell, chief executive of the Resolution Foundation, said: "Jeremy Hunt's first Budget was a much bigger affair than many expected, combining improvements to the dire economic and fiscal outlook with a significant policy package aimed at boosting longer-term growth in general, and the size of the workforce in particular.
"A step change in childcare support stands out."
He added: "But stepping back the UK's underlying challenges remain largely unchanged. We are investing too little and growing too slowly.
"Our citizens' living standards are stagnant. We ask them to pay higher taxes, while cutting public services. No one Budget could turn that around, but it's time Britain did."
