When Cabinet meets on Tuesday, Mr Johnson will call on colleagues to promote existing support measures and help people into high-quality and well-paid work.
No 10 said in a statement that the Government was renewing efforts to raise awareness of the “strong package” of assistance already on offer, from which it said thousands may be missing out.
“High levels of public debt following the unprecedented support provided during the pandemic, together with rising inflation and interest rates, mean we must maintain control of the public finances rather than burden future generations with higher debt,” it said.
It added Cabinet was also clear that “private companies must play their part”.
“Ministers won’t hesitate to crack down on unacceptable behaviour taking place within industry, where they are unfairly pushing up bills further for hard-working people,” it said.
It comes as Labour has warned Britons are facing a £10 billion hike in annual petrol and diesel costs, with “soaring” prices putting the squeeze on working families.
The party reiterated its call for an “emergency budget” to tackle the cost-of-living crisis, with a cut to energy bills funded by a windfall tax on oil and gas companies.
Ahead of Cabinet, Mr Johnson said: “With household bills and living costs rising in the face of global challenges, easing the burden on the British people and growing our economy must be a team effort across Cabinet.
Easing the burden on the British people and growing our economy must be a team effort across Cabinet
Boris Johnson, Prime Minister
“We have a strong package of financial support on offer, worth £22 billion, and it’s up to all of us to make sure that help is reaching the hardest-hit and hard-working families across the country.
“We will continue to do all we can to support people without letting Government spending and debt spiral, whilst continuing to help Brits to find good jobs and earn more, no matter where they live.”
Ridiculing the PM’s call to action, Lib Dem leader Sir Ed Davey said the Government was “completely out of ideas”.
“Whilst families are facing sky-rocketing bills and soaring inflation, Boris Johnson’s answer is another quiz night at No 10,” he said.
“What the British people need now is proper leadership – that means an emergency budget, a cut to VAT and a windfall tax on the super profits of the oil and gas companies.”