Addressing the annual Tory party conference today, Mr Sunak also promised to restrict the availability of vapes under plans to "put the next generation first".
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Ministers have faced repeated calls to ban vapes to help protect children and reduce the significant environmental impact of the single-use products.
It commissioned a review, published last June and led by Dr Javed Khan, which made a series of recommendations, including increasing the legal age for buying tobacco.
Cancer Research UK's chief executive Michelle Mitchell said: "Raising the age of sale on tobacco products is a critical step on the road to creating the first ever smoke-free generation."
"Future generations of adults who are considered old enough to vote, pay taxes, drive a car and drink alcohol are going to be treated like children and denied the right to buy a product that can be purchased legally by people a year older than them."
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