Badenoch arrived in Birmingham's Symphony Hall with a message to Conservative Party members that they face a "battle for the soul of the this nation".
She argued her party is "renewed" and "coming back" as she continued efforts to convince voters that it has changed following an historic defeat at the 2024 general election.
In a nod to those who have defected to Nigel Farage's party, Badenoch said: "The Conservatives have had an export boom of drama queens going to Reform.
"This party is now the no drama party, we are the no-nonsense party."
With the party trailing Labour and Reform in the polls, Badenoch acknowledged that people are "looking through the shop window", they "like what they see" but "not enough of them are buying yet, we need to fix that".
Her inspiration for how to revive a long-standing brand was Marks and Spencer (M&S), saying they have "adapted their style for today's market and people are flooding back".
Badenoch added: "Just like M&S, we must learn from our mistakes, win back trust and make people feel good about our party again."
One of the biggest responses in the room from members came as Badenoch made clear she did not want to do an election deal with Reform.
She described many Reform voters as "our people", adding: "We let them down and we want them to come back home."
Following a section of the speech mocking some of Reform's senior figures, Badenoch said: "To those who say 'unite the right', we are not uniting with that.
"People deserve better than that and we are going to give them better than that. Character, conduct, and standards matter."
She also said she did not want to live in a country run by people who "debate whether my mixed-race children are English".
In one of many jibes aimed at Burnham, Badenoch labelled him a "Paddington Bear prime minister" who was "hoping that the problems will just go away".
In the days ahead of Wednesday's speech, there was widespread speculation that Badenoch would announce changes to IHT.
As the opposition leader neared the end of her 66-minute speech, she said IHT was "supposed to be a tax on the super wealthy" but it is "now a tax on ordinary middle-class families in every corner of our country".
She said: "The next Conservative government will legislate so nobody will ever pay inheritance tax on their family home.
"On top of that, couples would be able to leave an additional £1m tax-free and these changes mean every inheritance tax bill will be cut and the number of families paying inheritance tax will fall by more than half."
The Conservatives have estimated the policy would cost around £6bn a year and believe they have identified £71bn of savings that can be made to government spending, including welfare cuts.
Under the current rules, estates worth more than £325,000, or £500,000 if a home is left to children or grandchildren, can face a 40% tax rate on assets above the threshold.
Married or civil partners can also transfer assets between each other.
In 2023-24, 4.72% of UK deaths resulted in an IHT charge and raised around £7bn for the government.
Badenoch also said her "ambition is to abolish inheritance tax altogether, as soon as we can afford it".
Labour Party chairwoman Bridget Phillipson said: "The Tories haven't changed.
"Kemi Badenoch has shown that the Tories' choice is to do nothing to help ordinary families struggling with the cost of social care, prioritising the wealthiest instead."
Reform UK economy spokesman Robert Jenrick said Badenoch had "chickened out of doing anything big" and is "for the 2%".
The former Tory MP said: "While the Tory Party is offering handouts to multi-millionaires, Reform will give everyone a £500 tax cut by raising the tax-free personal allowance to £15,000.
"The Tory Party is looking after its own in Kensington, Reform is looking after the country."
Elsewhere in her speech, Badenoch referred to other policies the party has announced in recent days.
These include a £10bn anti-missile defence system, 50,000 new prison places and halving the rate of employer national insurance on earnings for people aged between 21 to 24.
They also pledged to scrap the "cliff edge" that means parents in England lose out on childcare support when they earn more than £100,000 a year.
Another policy to be scrapped would be the High Value Council Tax Surcharge (HVCTS), dubbed the "mansion tax".
This is due to take effect from 2028 and introduces an extra levy for owners of properties in England valued at more than £2m.
Liberal Democrat leader Sir Ed Davey responded to the speech by saying Badenoch had been "lecturing the country on fiscal responsibility while making tens of billions in unfunded promises".
Green MP Carla Denyer added: "Kemi Badenoch once again defined the Conservative Party as pro-billionaires, pro-inequality and pro-damaging the environment." %!s()
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