In a cautious set of tax and spending plans, Healey said he would raise taxes on banks, gambling, savers and landlords while also tightening value-added tax rules for online marketplaces such as Amazon and eBay.
That would help to fund the cost-of-living package and some property tax relief to small businesses.
Healey warned about the effects of the conflict in the Middle East, which has driven up oil and gas prices, as well as from trade tensions and the war in Ukraine.
"Those are the storms we face. We can't wish them away. We must choose the course we steer through them," he told parliament in his first fiscal address.
On entering Downing Street in July, Burnham promised "the biggest changes in the last 40 years" in politics in the United Kingdom, including a bigger role for the state in the economy.
But he and Healey, a former trade union official, have to tread carefully to avoid piling more bond market pressure on the government.
Borrowing costs have risen globally this year, ensnaring countries like France which is struggling to shore up its finances amid a wave of social unrest.
The new budget measures included a 100 pound ($A190) payment to about 20 million households living in lower-valued homes to soften a leap in their energy bills, costing 2.6 billion pounds.
Healey also said he would support drivers by keeping a freeze on the level of fuel duty rates until at least July at a total cost of 1.4 billion pounds over the period.
The UK's budget forecasters said the plans, combined with higher inflation and borrowing costs, would add 65 billion pounds to borrowing over five years and slow the pace of fixing the public finances in the near term.
The Office for Budget Responsibility warned that living standards would fall before edging only fractionally above their level before the COVID-19 pandemic by the end of the decade.
"It's a pretty grim picture," OBR official David Miles told reporters.
David Aikman, director of the National Institute of Economic and Social Research think tank, said energy prices and borrowing costs might not fall back after 2027.
"If the bet comes up tails, the chancellor will have to change course and cut spending or raise taxes," Aikman said.
But investors took comfort from Healey's relatively low-key plans - with time limits on the support measures - after two big-tax big-spend budgets of his predecessor Rachel Reeves.
Shares in banks rose on relief that the 1.5 billion pound hit to the sector was not bigger.
A levy on profits will rise by three percentage points to six per cent for 15 months, less than the five percentage point increase some equity analysts had expected.
Healey also announced gambling taxes will be hiked to pay for a high street support package, including by increasing machine games duty from 20 per cent to 25 per cent for higher stakes machines.
He said it would mean that 70,000 businesses would be taken out of paying rates altogether "meaning half of our shops, restaurants and gyms will now pay no business rates at all".
Other budget measures included removing standing charges on gas bills to help most households and extending tariff cuts on some imported goods including gherkins and marmalade.
More than 20 billion pounds in extra support will go to state finance institutions to spur investment in artificial intelligence, the military and green energy by the early 2030s.
Regional mayors will gain more control over tax revenues to further Burnham's devolution push.
with PA
