Failure to tackle drug-resistant infections will lead to at least 10 million extra deaths a year and cost the global economy up to $100tn (£64tn) by 2050, a report commissioned by David Cameron, the prime minister, has warned.

The stark figures, published on Thursday, and believed to be the first to quantify the potential impact of antimicrobial resistance (AMR) – drug-resistant infections or superbugs – will be used to make the case to global leaders that urgent action is needed. To put the figures in context there are currently 8.2 million deaths a year from cancer and annual global GDP stands at $70tn to $75tn, with the UK figure around $3tn.

Former Goldman Sachs chief economist Jim O’Neill, who chaired the report, said AMR represents a more certain threat than climate change in the short term. “We cannot allow these projections to materialise for any of us, especially our fellow citizens in the Bric (Brazil, Russia, India, China) and Mint (Mexico, Indonesia, Nigeria, Turkey) world, and our ambition is such that we will search for bold, clear and practical long term solutions,” he said.

The report is the first published by the Review into AMR, set up by Cameron in July, amid growing concerns about the scale of the problem. It acknowledges that the human impact should be enough to prompt major intervention but says the economic figures illustrate that the issue “transcends health policy”.

Modelling by KPMG and RAND Europe, commissioned by the review, looked at three bacteria – K pneumoniae, E coli and Staphylococcus aureus – out of a group of seven highlighted by the World Health Organisation, as already showing concerning resistance levels.

It also examined HIV, tuberculosis and malaria as broader public health issues for which resistance is a concern.

No country is considered immune from the threat but for some regions and nations the outlook is particularly bleak. The world’s most populous countries, India and China, face 2 million and 1 million deaths a year respectively by 2050 and one in every four deaths in Nigeria by then is forecast to be attributable to AMR. Africa as a continent “will suffer greatly”, the report warns.

A “low estimate” of the current number of annual global deaths is put at 700,000.

O’Neill said of the $100tn figure ($15tn of which is from Europe): “As big as that number seems it almost definitely underestimates the economic cost.”

He explained that this was because the study looked only at a subset of drug-resistant bacteria and public-health issues and did not examine the social costs, the demand on national healthcare systems and secondary health effects – the danger that interventions that have become routine in the developed world which rely heavily on antibiotics could be severely undermined. Caesarian sections, joint replacements and chemotherapy, by keeping people economically active, could together account for another $100tn between now and 2050, according to the report, although that amount would not be completely lost.

Despite the grim prognosis, O’Neill said there is hope if international consensus is reached and through advances in diagnostics, stimulating the development of new AMR drugs and alternative therapies such as vaccines – interventions which will be explored in greater detail by the review in future papers.

“With modern technology and the right focus and right guidance, by trying to leverage the world’s greatest technology for diagnostics, it would probably make significant difference to the pressure for use of antibiotics,” he said.

Professor Dame Sally Davies, chief medical officer for England, said: “This is a compelling piece of work, which takes us a step forward in understanding the true gravity of the threat. It demonstrates that the world simply cannot afford not to take action.”

• This article was amended on 11 December 2014. It originally stated that the UK’s annual GDP was £3bn. It is £3tn. This has been corrected.

