Mr Hammond said: "'My idea of ending austerity does not involve increasing people's tax bills". He said that taken as a whole, other departments would see their spending rising in line with inflation.
He said: "I think people will be crushingly disappointed at yesterday because it certainly wasn't the end (of austerity)".
But he added: "On wider definitions, it doesn't, at least not yet".
Asked if Labour would reverse the Government's planned tax cuts, Mr McDonnell told Today: "We will support the tax cuts at the moment on the basis that it will inject some demand into the economy".
"If I were a prison governor, a local authority chief executive or a headteacher ... I would be preparing for more hard years ahead".
Setting out his income tax cuts, Mr Hammond said the personal allowance will rise to £12,500 from April 2019 and the higher rate threshold will rise to £50,000.
The service is part of the NHS 10-year plan, and will be covered by the £20.5 billion of government funding per annum, announced by Theresa May back in June.
Mr Johnson said there would be "millions of losers" from the introduction of Universal Credit, despite an injection of around £2bn per year to ease the transition to the controversial new benefit.
Chancellor Philip Hammond's "rabbit out the hat" tax cut on Monday was well received, and rightly so as it does put some welcome extra cash in many people's pockets in the crunch time for Brexit.
"Now we know", he said.
But while global tech firms will face a new tax, Mr Hammond promised a package of help for the nation's high streets which have suffered as shoppers have moved online.
"Yes, the OBR reduced borrowing forecasts so he was able to find more money without committing to more borrowing".
And by his arbitrary action to raise duties on wines but not on beer or spirits he has again demonstrated that alcohol is an easy target for a chancellor looking to raise revenue.
"Suppose the public finance forecasts deteriorate significantly next year". 'There is one stand-out example of where the rules of the game must evolve now if they are to keep up with the emerging Digital Economy, ' Hammond told Parliament. "What will he do then?"
Perhaps the biggest question is "why Hammond sought to bring forward tax giveaways via raising the thresholds", says Sky News's Ian King, who notes that "these are the kind of things that are normally done by a chancellor in an election year".
"He's going to struggle to reimpose austerity having announced its end".
Meanwhile, public spending is set to remain on a relatively tight leash even after the government's so called "giveaway", with total expenditure estimated at £812.8 billion in 2018, before rising to £955.3 billion in 2023.
Improved deficit and upgraded growth forecasts allowed the Chancellor to loosen the purse strings, releasing more than £100billion to cut taxes and increase spending.