They say workers without the equivalent of five GCSEs should have the right to paid time off to study. Some 35 per cent of companies do not support any training.
The report, 2020 Vision for Skills, aims to influence Lord Leitch's review of the future of skills this autumn.
It argues that eradicating low skills by 2020 will depend on improving adult vocational education, but that not enough employers are supporting existing programmes for training.
"We will not achieve this until we accept the existing voluntary skills framework is no longer fit for purpose," the report says.
More than a million 50 to 65-year-olds who want to work are unable to do so because employers will not recruit or train older people, or make adjustments for people with disabilities, it says.
It suggests there should be Government targets for participation in vocational education as well as in higher education, to give a stamp of approval to the non-academic route. And employers who offer training should be given tax breaks, the report says.
Paul Mackney, joint general secretary of the University and College Union, said: "The Government's new funding strategy for adult education is based on the assumption that employers will pay more towards training but this report confirms there is still a lot of ingrained resistance.
"The Government must secure a statutory basis for workplace training which would in turn create a new training culture."
But Anthony Thompson, head of skills at the Confederation of British Industry, said unions should acknowledge that business already invests pound;33 billion in training. He said: "We have got to focus on the goal of increasing productivity. All-encompassing regulation would not actually recognise the diverse nature of the workforce and of the economy."