The contender for the leadership also suggests she would take the winter fuel payment off hundreds of thousands of pensioners while Mr Sunak and Tom Tugendhat also launch their campaigns.
The former minister, who resigned from Boris Johnson’s government last week, also proposed means-testing hundreds of thousands of pensioners to take winter fuel payments because there are some “who can afford it”.
Rishi Sunak has wrongly made “inefficient” one-off payments to help people struggling with the cost of living crisis, said Conservative leadership contender Kemi Badenoch.
Ms Badenoch, whose insurgency campaign is gaining momentum after finishing second in a leadership poll of Tory members for ConservativeHome on Tuesday, said her priority in fixing the cost-of-living crisis was tackling inflation through “system change”.
Earlier in its campaign, the right said it would cut taxes but also significantly reduce the size of the government to pay for it, insisting there should be “no free lunches, no tax cuts with no limit on government spending, no stronger defenses without a slimmer state”.
Asked how she would tackle the cost-of-living crisis, Ms Badenoch suggested she could start with Mr Sunak’s recent £15bn support package.
Ms Badenoch said: “I think if we focus on the things that government should be doing…we’re going to make things easier for people in the short, medium and long term.
“What I’m not going to do is put out a lot of micro-policies to give people £50 cash here or a discount there. I think it’s very inefficient, there’s a lot of baggage in the way we work government.
“I have people in my constituency who tell me they don’t need the winter fuel payments we give them because they can afford it. Why don’t we have a more sophisticated means testing mechanism?”
During his own start, Mr Sunak, the bookies’ favourite, refused to announce concrete policy plans and lashed out at rivals over promises to abolish taxes – including increases in national insurance – which he had voted to support during his time in Cabinet .
He said: “I’ve had to make some of the toughest decisions of my life as Chancellor, particularly how to manage our post-Covid debt and credit. I’ve never hidden from it, I’m certainly not going to pretend now that the decisions I made and the things I voted for were somehow unnecessary.”
The former chancellor called for a “new consensus” on immigration with better access for highly skilled foreigners, but declined to commit to increasing defense spending.
He insisted that stepping down from Boris Johnson’s cabinet was “incredibly difficult” and said the outgoing Prime Minister was “one of the most remarkable people I’ve ever met” and “have a good heart”.
He also vowed not to assign Dominic Cummings a role in his government and claimed not to have spoken to the former No10 adviser since Mr Cummings left Downing Street.
Elsewhere, Tom Tugendhat, another contender for the Tory leadership, said he would call in the military to tackle the NHS backlog on his first day as Prime Minister and reintroduce mandatory waiting time targets for A&E.
He also said he would scrap the increase in Social Security – which funds the health and welfare levy – but sources insisted tackling social care would remain a priority.
Mr Tugendhat also promised a 10p fuel tax cut and guaranteed lower taxes for businesses.
He laid out a 10-year economic plan and said he wanted to cut government costs where possible and cut taxes across the board.
But he stopped promising more personal tax changes as sources said he wanted to avoid a “race to the bottom on tax cuts.”
Mr Tugendhat, a former army officer who has yet to hold cabinet office, denied he would be in the race to land a job in someone else’s government – insisting he “wanted to run the country I love “.