Under current pricing, a packet of 10 cigarettes cost about £3, compared to nearly £6 for 20.
Last week the Scottish Government announced a range of proposals to restrict tobacco sales in Scotland - including a ban in shops from displaying cigarettes in "pride of place" on their shelves.
On the latest consultation document, Public Health Minister Dawn Primarolo said it was vital to take away temptation from children.
"Protecting children from smoking is a government priority and taking away temptation is one way to do this," she said.
"If banning brightly coloured packets, removing cigarettes from display and removing the cheap option of a pack of 10 helps save lives, then that is what we should do, but we want to hear everyone's views first."
Martin Dockrell, from the anti-smoking group Action on Smoking and Health (Ash), said: "These sorts of measures are not going to have an overnight effect, but we think they will over time."
A YouGov poll commissioned by Ash of 3,330 people found that 65% supported a complete ban on cigarette vending machines, while 43% favoured the introduction of plain packaging.
As far as vending machines go, the simple solution is to make them credit card operated - then children can't use them
It applies in its entirety to England, and certain sections - including that on smoking and young people - apply to Wales and Northern Ireland.
The plans come as the World Health Organisation (WHO) called on governments to ban all tobacco advertising to help prevent young people taking up the habit.
The Tobacco Manufacturers' Association said it "completely agrees with the government that children should not smoke and should be actively discouraged from doing so".
But its director, Chris Ogden, added: "While we welcome any sensible proposals that will assist in preventing the sale of tobacco to children under the age of 18, any proposals should be supported by credible evidence that they would address the government's stated objectives."
Smokers' lobby group Forest warned that banning point-of-sale display could make smoking even more attractive to teenagers, and could increase the appeal of counterfeit and smuggled cigarettes.
Spokesman Neil Rafferty said: "In one Canadian province, youth smoking actually went up in the first 18 months after a display ban was introduced.
"As far as vending machines go, the simple solution is to make them credit card operated - then children can't use them."
He criticised plans to ban packs of 10, arguing that children could still afford packs of 20.
One newsagent told the BBC he was dismayed by the proposals.
Phillip Youle, from Bridgewater, said: "Just how are my customers supposed to know what I have in stock and the price, if I am forced to take them off display and put them under the counter?
He went on: "Is the government going to pay for the costs involved to adapt my counter? Will they compensate me for the inevitable loss in trade?
"Its hard enough to make a living in this game as it is; these proposals will see many newsagents/corner shops close."
The proposals follow a series of restrictions on smoking in the UK which have come into force over the last couple of years.
The legal age for smoking was raised from 16 to 18 in October.
A ban on smoking in public places and workplaces in England came into force last July.
Bans were introduced in Scotland in 2006, and in Wales and Northern Ireland in 2007.
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