The parliamentarians also say taxes should be raised on cigarettes to make them more expensive and put people off - helping to create a ‘smoke-free’ generation.
The All Party Parliamentary Group on Smoking and Health said are also calling on big tobacco companies to be charged for the impact they have on society - with the millions raised going to stop-smoking initiatives.
Its chairman, the Conservative MP Bob Blackman, said: "Smoking remains the leading cause of premature death and health inequalities.
"Ratcheting up tobacco regulation further and faster is essential to achieve the Government's vision for prevention, to increase healthy life expectancy by five years by 2035 while reducing inequalities between the richest and poorest in society."
Other measures proposed by the group include:
- Banning the sale of tobacco from unlicensed retailers or those who break laws on who should be sold to.
- Collection and publication of tobacco manufacturers' sales and marketing data.
- Spending more on educational campaigns and making manufacturers insert stop-smoking information cards inside packs.
- Tightening rules on smoking in television programmes and films.
The group proposed raising the smoking age, as people over 21 are less likely to experiment with smoking, which later turns into a habit.
Meanwhile "Big Tobacco" firms should be charged a "polluter pays" levy to pay for the costs of tobacco control, which could raise £150 million, and taxes on tobacco should be raised to 5 per cent above inflation, with an equal surcharge added to both loose tobacco and manufactured cigarettes.
Lord Rennard, a vice-chairman of the group, said: "Tobacco manufacturing is by far and away the most profitable consumer industry in the world,and Big Tobacco can certainly afford to pay more to clear up the devastating damage its products cause."
Deborah Arnott, chief executive of Action on Smoking and Health - which assists the group, said: "Legislation to strictly regulate smoking used to be considered controversial and extreme by all mainstream political parties. Thanks to the dedication of the All Party Group, working closely with civil society, that's no longer the case.
"Governments now have confidence that tough tobacco regulation both delivers results, and, crucially, has widespread cross-party and public support."
The British Lung Foundation welcomed the recommendations. Chief executive Penny Woods said: "A 'polluter pays levy' could raise at least £150 million. This money, which the highly profitable tobacco industry can easily afford, could fund cash-strapped stop-smoking services and discourage young people from ever lighting up.
"The recommendations will also protect children by funding enforcement against underage sales and help tackle the trade in illicit cigarettes.
"Raising the age of sale from 18 to 21 will help stop experimentation from becoming a fatal habit and reinforce the dangers of tobacco.
"The next step is for the Government to show its commitment to achieving a smoke-free generation by adopting the full list of recommendations and turn them all into law."