Anti-smoke campaigners claim the majority of people would support greater controls on tobacco.
The Government launched its consultation, "The Future of Tobacco Control", on Saturday, which proposes plain cigarette packets with no branding or logos, minimum pack sizes of 20, pushing sales under the counter and a ban on vending machines.
A YouGov survey of 1,056 adults, commissioned by Ash, revealed that 65% were in favour of a vending machine ban and 59% in favour of a ban on tobacco displays at point of sale.
But 79% were in favour of simply restricting vending machines to age restricted venues and only 43% were in favour of the introduction of plain packaging for tobacco products.
Other results showed:
• 77% in favour of banning smoking in cars carrying children under-18• 60% in favour of increasing tobacco prices faster than inflation rate• 74% in favour of increasing local stop smoking services
"Smoking is a habit which is passed down from generation to generation and this pattern can only be broken by fresh thinking and a comprehensive cross-government strategy," said Ash director Deborah Arnott.
"The Smokefree Action Coalition welcomes the Government's consultation on a national tobacco control strategy and its focus on the need to protect children and reduce health inequalities.
"This is also popular with the public - the YouGov poll shows strong support for tough measures to protect children from the harm caused by tobacco."