Rishi Sunak's bill aims to create the UK's first smoke-free generation in a major public health intervention.
The Tobacco and Vapes Bill would ensure anyone turning 15 from this year would be banned from buying cigarettes, and also aims to make vapes less appealing to children.
A number of Tory MPs have told the BBC they won't back the bill.
Conservative MPs will get a free vote on it so they won't be ordered to vote with the government, but the bill is likely to pass as it has Labour support.
The bill would make the sale of tobacco products, rather than the act of smoking, illegal.
Tobacco use is the UK's single biggest preventable cause of death, killing two-thirds of long-term users and causing 80,000 deaths every year.
On top of that, a patient is admitted to hospital with a smoking-related condition, such as heart disease, strokes and lung cancer, almost every minute in England.
Supporting the ban, England's chief medical officer Professor Sir Chris Whitty said once people become addicted to smoking "their choice is taken away".
"If you are in favour of choice you should be against something that takes away people's choice.
"When I was a junior doctor doing surgery I remember the tragedy of seeing people, whose legs had had to be cut off because of the smoking that had damaged their arteries, outside the hospital weeping as they lit up because they were trapped by addiction - that is not choice."
Tory MP Sir Simon Clarke, who served in Liz Truss and Boris Johnson's cabinets, said he did not support the move.
He told BBC Radio 4's Today programme it was far better to focus on education and the tax system to deter young people from smoking, rather than enforcing an outright ban.
"[An outright ban] risks making smoking cooler, it certainly risks creating a black market, and it also risks creating an unmanageable problem for the authorities," he said.
I've never smoked.
I don't like being near cigarette smoke.
I support the right of people to smoke.
This is about control vs freedom. The government cares naff all about our health.
@GeldingEmilyLibertarian2wks2W
Far more people die from obesity than they do from cigarettes yet The mainstream media seems to be encouraging people to be fat. Fat acceptance is not good I don't think people should smoke but they have every right to do so
@CabinetDuckForward2wks2W
That's not a reason not to ban cigarettes. And also it's not possible to ban obesity. Sure, you could ban certain types of processed foods but I'm not convinced doing so is a good way to tackle obesity.
@ISIDEWITH2wks2W
@DopeySalamiDemocrat2wks2W
The Bill won’t prevent anyone who does smoke from smoking.
The Bill is about stopping children from ever starting
Smoking causes 150 cancer cases a day.
That’s why o support the Bill.
@ISIDEWITH2wks2W
@ISIDEWITH2wks2W
@ISIDEWITH2wks2W
@ISIDEWITH2wks2W
Ooooh, 19 now when we already refuse people who look under 25 for them....genius. and then adding a year for each year.....Look out people, we have a scale that means in 30 years only 60 plus can buy cigs!
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