The law would ban the selling of tobacco products to anyone born after January 1, 2009 –- effectively raising the smoking age by a year each year until it applies to the whole population.
"This has the potential to phase out smoking in young people almost completely as early as 2040," the government said when it unveiled the plan, calling the move "historic".
While the law looks set to pass thanks to support from opposition parties -- including Labour, which is expected to win a general election due this year -- Sunak faces the prospect of a rebellion from backbench Tory MPs.
The beleaguered leader has little political capital to expend within his fractured party as he struggles to revive its fortunes following months of dire polling.
Smoking is the UK's biggest preventable killer and opinion polls show that around two-thirds of people in the UK back a phased smoking ban.
However, libertarian-leaning MPs on the right of the ruling Conservatives, including former prime minister Liz Truss, have branded the move an attack on personal freedoms.
Conservative MP Simon Clarke told BBC radio that he was "both sceptical and downright opposed" to the plans.
"I think that an outright ban risks being counterproductive, I think it actually risks making smoking cooler, it certainly risks creating a black market, and it also risks creating a unmanageable challenge for the authorities," he said.
Former prime minister Boris Johnson also said at an event in Canada last week it was "mad" that the party of Winston Churchill was "banning cigars".
Vaping clamp down
Opening the debate for the government, Health Secretary Victoria Atkins told the House of Commons that there is "no liberty in addiction".
"Nicotine robs people of their freedom to choose. The vast majority of smokers start when they are young, and three quarters say that if they could turn back the clock they would not have started," she said.
MPs are due to vote on whether to approve the plans for the next stage of the legislative process on Tuesday evening.
Conservative MPs have been given a free vote, meaning they are able to defy the government without fear of being suspended from the party.
Westminster watchers will closely study the size of the rebellion to see what it suggests about Sunak's authority, amid reports that some cabinet members are considering voting against.
The proposed ban was supposedly inspired by a similar plan in New Zealand which was later dropped.
Official figures show smoking causes about one in four deaths from cancer and leads to 64,000 deaths in England per year.
"If parliament passes this new bill, it will put the UK at the very forefront of the fight to eradicate one of the most harmful inventions of modern times," said Lion Shahab, co-director of the tobacco and alcohol research group at University College London.
The legislation also seeks to clamp down on young people vaping by restricting flavours and packaging to make less appealing to children.
