The #coughup campaign is aimed at 16- to 24-year-olds and was created by youth agency, Livity.
The agency drafted in world-renowned spoken word artist Suli Breaks to highlight how smoking has an impact on the NHS, illness and lost days at work.
Cancer Research is aiming to secure 10,000 signatures for a petition, which asks the Government to add a tax levy of 1p per cigarette sold in the UK. This would help the Government raise an extra £500m, which could be invested in health services, the charity claims.
"It’s time for Big Tobacco to Cough Up and pay for the damage they cause," Cancer Research said.
"On 16 March, Chancellor George Osborne will outline the nation’s finances for the next year in his Budget. We want him to introduce a levy on the tobacco industry to pay for stop-smoking services."