(Adds details from briefing paper in paragraphs 3 and 7; shares in paragraph 11; company responses in paragraph 12)

MANCHESTER, England, Oct 4 (Reuters) - British Prime Minister Rishi Sunak on Wednesday proposed banning younger generations from ever buying cigarettes, a move which would give Britain some of the world's toughest anti-smoking rules.

The proposals - if they pass into law - would make Britain the first country in Europe to ban cigarette sales to younger people. Denmark is considering a similar move.

They could phase out smoking among young people almost completely as soon as 2040, a government briefing paper with details of the proposals said.

"A 14-year-old today will never legally be sold a cigarette," Sunak told the Conservative Party conference of his proposed new rule.

Under his anti-smoking plan, Sunak said the smoking age would be raised by one year every year, meaning a younger generation could grow up "smoke free", improving the country's health.

Sunak also plans to bring forward measures to restrict the availability of vapes to children.

The government will consult on restricting the flavours and descriptions of vapes so that they can no longer be targeted at children, the briefing paper said, adding the government would also look at regulating vape packaging and presentation.

The proposed smoking ban is similar to one brought in by New Zealand last year, which became the first country to stop those born during or after 2009 from legally buying cigarettes. The ban would take effect in 2027.

Sunak said smoking costs Britain's health services 17 billion pounds ($20.6 billion) a year and cancer deaths could fall by a quarter if people stopped smoking.

The policy would hurt companies that earn a relatively large portion of earnings from their British cigarette businesses, namely Japan Tobacco, maker of Camel and Benson & Hedges, and Imperial Brands, which produces Winston cigarettes and Golden Virginia rolling tobacco.

Shares in Imperial Brands fell 1.5% at 1209 GMT to their lowest since April 2022, while shares in British American Tobacco, which has a lower exposure to the British market, were down 0.8%.

Imperial Brands and rival tobacco companies either did not immediately comment, or declined to comment. ($1 = 0.8247 pounds) (Reporting by UK bureau and Emma Rumney; editing by Michael Holden, Sachin Ravikumar and Alex Richardson)