The report also found only 45% of UK workers had access to occupational health support from their employer.
Employers spent £900m on this, but only 27% of workers with long-term health conditions who used these services found it helped their employer provide support.
There were gaps in quality and access, especially for small and medium-sized organisations.
The Fabian Society said a national service would give everyone access to good quality support from both public and private sectors, overseen by a new occupational health authority within the health and safety executive.
Funding would come partly from a new health element added to the planned growth and skills levy, paid by the biggest 10% of employers.
Additionally, the report called for more support and incentives for employers and workers, alongside clearer rules on reasonable adjustments and better statutory sick pay.
Sasjkia Otto, report author and Fabian Society senior researcher, said: “Many employers spend a lot of money trying to keep their workforce healthy.
“But the UK’s failing occupational health system means they do not see return on their investment.
“Others fall short of the law because their duties towards workers are unclear and inconsistent.”
Otto added: “A national occupational health service would be a win for everyone involved – workers, business and the Government – ensuring everybody who needs it can access quality professional advice and support, and that workers are healthier and happier as a result.
“Nye Bevan, the architect of the NHS, was inspired by the free healthcare workers received in the mining community where he grew up.
“As people face new health pressures rooted in the workplace and beyond, it is time to revisit Nye’s lost legacy.
“The ongoing government review into healthy and inclusive work, led by Sir Charlie Mayfield, presents a generational opportunity to get this right.”
Christina McAnea, general secretary at UNISON, said: “Prevention is always better than cure.
“Hundreds of thousands of people leave the workforce for preventable health reasons, often never to return.
“But tackling issues at an early stage so people are happier and healthier is the best way to keep them engaged in their work for longer.”
McAnea added: “Establishing a national system to boost the economy is a no-brainer. It’s a win for workers, their employers and the UK economy as a whole.”
Sir Charlie Mayfield, from the Keep Britain Working review, said: “I welcome the work the Fabian Society have done on this critical issue.
“Their diagnosis of the situation, and the impact it is having resonates and reinforces many of the findings of the keep britain working review.”