In the first parliamentary vote on the proposals, 415 MPs voted in favour of taking the bill to the next stage of the legislative process, while 47 MPs voted against.
The UK Tobacco and Vapour Bill will prevent anyone born after 1 January 2009 from smoking legally by gradually increasing the age at which tobacco can be bought.
The government said its aim was to create the first "smoke-free generation" in Britain, AFP reported.
The proposals come after New Zealand scrapped plans to introduce a so-called "generational smoking ban" that would have stopped the sale of tobacco to anyone born after 2008.
The UK legislation is similar to a bill proposed by the last Conservative administration, which was shelved earlier this year when then Prime Minister Rishi Sunak called a general election.
However, the new Labour government of Sunak's successor, Keir Starmer, has reinstated the proposals, which are part of a drive to strengthen preventative health measures and reduce long-term pressures on the UK's state-funded National Health Service (NHS).
It also gives the Government powers to extend the scope of the indoor and outdoor smoking ban - playgrounds, outdoor spaces of schools and hospitals are being considered for consultation in England.
The Bill would introduce restrictions on advertising and sponsorship of e-cigarettes, as well as restricting the flavours, displays and packaging of e-cigarettes to reduce their appeal to children and young people.
It also proposes a ban on the manufacture and sale of oral tobacco - small packets that are placed under the lip - in line with European Union countries other than Sweden.
The government has also announced that disposable e-cigarettes will be banned next year by separate legislation.
"The Tobacco and Vapour Bill provides the protection children and young people need to avoid a life in prison from addiction," said Health Minister Wes Streeting.
England, Wales and Northern Ireland banned smoking in indoor public places and workplaces in 2007 following a similar ban in Scotland in 2006 | BGNES