The All Party Parliamentary Group on Smoking and Health urged the Government to renew its efforts to drive down smoking rates and look at ways to force tobacco firms to pay for health campaigns.
It said a Government strategy on smoking is now a year overdue.
It added that local authorities in England are struggling to fund stop-smoking services due to financial cuts by central Government.
The study, which includes data from the charity Action on Smoking and Health (Ash), said “new ways” need to be found to cut smoking rates.
“The tobacco manufacturers, whose products cause so much health, social and economic damage, should make a greater contribution to mitigating that harm,” it said.
“The four major tobacco manufacturers remain among the most profitable companies on Earth, so they could certainly afford to do this.”
It added: “The Government should reconsider its decision not to proceed with a levy on tobacco manufacturers to fund measures to reduce smoking prevalence, in line with the principle that has been established by the soft drinks industry levy.”
The cost of smoking in England is thought to be at least £12.9 billion a year, including NHS, social care and lost productivity costs.
Social care costs are thought to stand at £1.4 billion annually, including £760 million to local authorities and £630 million worth of private care funded by individual people.
Smoking is the leading cause of early, preventable death in England and leads to almost 80,000 premature deaths every year.
Smoking levels are now at their lowest ever point, but almost one in five (18%) adults and 8% of 15-year-olds still smoke.
MP Bob Blackman, chairman of the All Party Parliamentary Group on Smoking and Health, said smoking is contributing to the current social care crisis.
“The situation will worsen if funding to local stop smoking services continues to be cut. Smoking is the leading cause of health inequalities in the UK so this puts at serious risk progress towards the Prime Minister’s ambition to reduce the burning injustice caused by inequality.”
Deborah Arnott, chief executive of Ash, said: “Smoking places an enormous pressure on our over-stretched health and social care system, not to mention the many thousands of carers who spend their lives looking after loved ones.”
Izzi Seccombe, from the Local Government Association, which represents councils, said: “Social care faces a funding gap of least £2.6 billion by 2020, and the Government needs to urgently inject genuinely new money into the support councils provide for our elderly and vulnerable residents.
“The cuts by government to councils’ public health grants of nearly 10% - approximately £530 million over five years - also threaten to undermine the good work councils are doing around smoking cessation.”
Simon Clark, director of the smokers’ group Forest, said: “To suggest that smoking is contributing to the social care crisis is nonsense.
“Smoking rates are at their lowest ever level yet smokers still contribute £12 billion a year in tobacco taxation, a sum that far exceeds the alleged cost of treating smoking-related diseases or providing social care.”
A spokesman for the Tobacco Retailers’ Alliance said: “Businesses involved in tobacco, including its retail, already contribute a huge amount in tax to pay for things like the NHS.
“Councils have seen a massive drop in people using their smoking services because of the emergence of ecigs and have reduced funding accordingly.
“This should be applauded as saving taxpayers’ money, not criticised.”