The shadow chancellor said Labour would make the top 5% "pay that bit more".
Mr Hammond eased up on the big squeeze, says the i, while the Daily Express reports that he promised even better times are ahead from a "double deal dividend" if Theresa May secures a trade agreement with the EU.
He said: 'We are not going to oppose it on the basis it will put more money in people's pockets'.
"So let's assume there is a Labour Government, would you reverse the tax cuts being planned?"
He added: "If I were a prison governor, a local authority chief executive or a headteacher I would struggle to find much to celebrate".
The IFS said it is not clear yet whether austerity is over.
Hammond is expected to make the announcement in his Budget speech later on Monday.
"Given the dominance of the US tech giants, it is hard to see the Trump administration taking kindly to the digital sales tax as the United Kingdom sets out its stall for the best possible trade deal with the US", Dan Neidle, a tax partner at law firm Clifford Chance told the BBC.More news: Red Dead Redemption 2 has the Biggest Opening Weekend in Entertainment History
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Theresa May said today that an early general election would not be in the national interest, insisting that yesterday's budget was not meant to pave the way for an early vote.
The chancellor bases his Budget on figures from the Office for Budget Responsibility.
But the vast majority of that will be the £20.5bn boost for the NHS - leaving other departments would only see their budgets rise in line with inflation - 0.0% increase.
The think-tank said Hammond would be thanking his "lucky stars" that improved public finance forecasts had allowed him room to hand out the money.
The Budget has been branded "a bit of a gamble" by a respected economic research group.
Andy Burnham, mayor of Greater Manchester, said when he heard that the party "would be backing Philip Hammond's tax cuts for the richest" it sent a "shiver down my spine".
"Any idea that there is a serious desire to eliminate the deficit by the mid-2020s is surely for the birds".