The chancellor also suggested that he is willing to make potentially big cuts to some areas of public spending, to get the country’s debt falling.
The budget documents spell out real-terms reductions to some government departments in the years to come.
The likelihood of the government following through was questioned by the respected independent number cruncher, the Institute for Fiscal Studies (IFS) this week.
But asked if he would make big cuts, Healey said: “We’ve already demonstrated we are prepared to take hard decisions about the priorities in government.”
Pressed on whether he would make cuts of more than 2% a year to some government departments, he added: “We will carry that through to the 10-year plan and the spending review next year.”
“But in the budget I also set out the ways that we’re preparing and the work we’ve got under way to prepare for those spending review decisions.”
Conservative Party leader Kemi Badenoch said the “bulk” of spending cuts should be from the welfare budget, describing it as containing “astronomical sums”.
She also proposed reducing the size of the civil service and reducing budgets in departments such as the Department for Digital, Culture, Media and Sport.
On whether she would support cuts pencilled in by the government, Badenoch told the same programme: “What exactly are they cutting? I’m not against what they’re doing but there’s no detail.”
Badenoch said she did not want to see cuts in frontline services but said there was a need to “bring down the cost of government”.
Reflecting on the Budget, she said: “The chancellor had 98 different measures, a lot of them very piecemeal, none will make a difference.
“So living within our means, absolutely, we’ve got to do that. That will require cuts to government, but we are setting out the things very clearly that we’re going to change, the bulk of which is in welfare. Other departments will have changes too.”