In a report released ahead of next week's Budget, campaigners are calling on Chancellor George Osborne to increase the tobacco "tax escalator" from 2% to 5% above inflation year on year.
The move would net the Government an extra £485 million in the first year and £7.4bn over the next five years, it said.
Furthermore, it said the number of smokers would fall by 104,000 in the first year, with a reduction in deaths from smoking of 479.
A 15% rise above inflation for hand-rolled tobacco would lead to even more lives saved, far fewer smokers and further revenue, it added.
The report, from the charity Action on Smoking and Health (Ash) and the UK Centre for Tobacco and Alcohol Studies, is backed by NHS groups of doctors, directors of public health, the Royal College of Paediatrics and Child Health, and the Royal College of Physicians.
Charities including the British Heart Foundation (BHF), Cancer Research UK, and the Roy Castle Lung Cancer Foundation also back the study.
It comes as a poll of more than 2000 former smokers for the BHF found 42% believed raising the tax on tobacco would help other smokers quit.
Over two in five (43%) said GPs should approach the subject more often with smokers during routine appointments, while 35% called for more information about local stop-smoking services.
Nearly one-third (30%) said reducing the number of smoking scenes in TV programmes and films would help people quit, while 34% wanted more information in gyms, offices and leisure centres.