Individual cigarettes could have “smoking kills” printed on them under a raft of tough measures proposed by MPs to encourage more people to quit the deadly habit.

MPs have submitted an amendment to the health and care bill going through parliament which would allow the health secretary to make graphic health warnings mandatory.

“We know that cigarettes are cancer sticks and kill half the people who use them. So I hope that health warnings on cigarettes would deter people from being tempted to smoke in the first place, especially young people,” said Mary Kelly Foy, the Labour MP behind the move.

“I hope it would encourage some smokers to give up because if they are putting that in their mouth and seeing that message on cigarettes every time they smoke, I hope it would have the desired effect.”

Cancer Research UK and the Royal College of Physicians, which represents hospital doctors, are backing the plan. Foy says only “bold action” will help the government achieve its ambition of England being smoke-free – where only 5% of people light up – by 2030.

The Conservative former Cabinet minister, Sir George Young, now a peer, has separately introduced a private member’s bill into the House of Lords seeking to ensure cigarettes have to carry such warnings, which could also say “smoking causes cancer”.

Cigarette packets already carry warning messages such as “smoking causes cancer” as well as images of people who are seriously ill in hospital with smoking-related disease. Foy also wants tobacco firms to be forced to include health information messages inside packets.

Deborah Arnott, chief executive of Action on Smoking and Health (Ash), said: “Warnings on cigarettes were suggested over 40 years ago by then health minister George Young. The tobacco companies, with breathtaking hypocrisy, protested that the ink would be toxic to smokers. The truth is cigarette stick warnings are toxic to big tobacco and this is an idea whose time has come.”

Conservative MP Bob Blackman has endorsed Foy’s amendment, as has the shadow health secretary, Jonathan Ashworth, and shadow justice secretary Alex Cunningham.

Foy’s amendments would also empower the government to impose a new levy on tobacco company profits, with the proceeds being used to fund stop smoking activities.

Blackman, the chairman of the all-party parliamentary group on smoking and health, added: “As the chief medical officer Prof Chris Whitty says, big tobacco is an industry which ‘kills for profit’. Profits are obscenely high, two to three times greater than companies selling consumer necessities like food and drink. Our ‘polluter pays’ levy is both necessary and justified.”

Foy’s amendments would also let the health secretary:

Raise the legal age for buying cigarettes from 18 to 21.

Stop e-cigarette makers using tactics that might entice children to try them, such as sweet flavourings and cartoon characters.

Make it illegal to give e-cigarettes away free as sampler products, as some manufacturers have done.

Simon Clark, the director of the pro-smoking group Forest, criticised the moves proposed by Foy. “Everyone is aware of the health risks of smoking. There are huge, impossible-to-miss health warnings on every pack of cigarettes, including grotesque images of smoking-related diseases.

“Tobacco is sold in standardised packing and banned from display in shops. Enough is enough. If adults still choose to smoke that is a matter for them, not the government.”

The proportion of adults in the UK who smoke has fallen over recent years to 14.1% – the lowest figure ever recorded – as a result of tightened restrictions on the marketing of cigarettes and campaigns reminding the public of the dangers they involve.

The Guardian approached the Department of Health and Social Care for its response.