Dr. John Britton, head of the Royal College of Physicians Tobacco Advisory Group, urged Health Secretary Andrew Lansley to begin working toward that goal, Sky News reported.
"Andrew Lansley could make himself a legacy greater than that of almost any other health secretary in history," Britton said. "I think it will be entirely realistic for all practical purposes to eradicate smoking within 20 years."
Smoking rates have dropped in Britain, where about 200,000 people begin smoking each year. Proposals to make the habit less attractive include requiring tobacco to be sold in unbranded packages.
Anti-smoking activists in Australia are pushing for a ban on sales of tobacco to anyone born after 2000, an some British activists are considering that proposal as well.
"Our vision is to make smoking history for our children in the next 20 years and we know there are millions out there that back this," Ailsa Rutter, chief executive of the British anti-smoking group FRESH, said.