Employers and colleges must understand each other's needs better to improve the quality of work training, MPs say.
Lack of skills is estimated to cost the UK £10bn a year
The Commons public accounts committee said colleges needed a "different mindset", while companies had to be "more demanding" about courses offered.
Chairman Edward Leigh said a modern economy simply cannot afford to leave millions of staff without training.
The government is setting up a network of 450 "skills brokers" in England to liaise between businesses and colleges.
Layer of bureaucracy
The Learning and Skills Council estimates that a lack of basic skills is costing the UK economy £10bn a year.
It will spend £30m to £40m a year on brokers from this September.
The committee warns that this could create "an extra layer of bureaucracy" and that the scheme should be used to "add value and reduce costs".
It advocates making workers generally more demanding, "so that they too can help persuade their employers of the benefits of training for competitiveness and enhanced productivity".
Mr Leigh said: "Employers naturally put their businesses first and so they need to be persuaded that releasing their employees for training makes business sense.
"Employers need access to straightforward, clear advice on where good quality, flexible training is available."
According to government figures, a third of firms are not carrying out staff training each year.
Official figures also say that 90% of employers who train workers use private companies, compared with 46% who use further education colleges.
The committee's report says of colleges: "Responding to employers' needs requires a different mindset and approach."
Those which do not respond "can damage the reputation of the college sector as a whole", it adds.
Employers in turn "can influence college training programmes by being more demanding about what they want from colleges".
Anthony Thompson, head of skills at the CBI, said employers took their responsibilities seriously.
He added: "But while employers can do more it is clearly the responsibility of government, not business, to ensure people of all ages have the reading, writing, arithmetic and communication skills to make their way in the world."
But Dr John Brennan, chief executive of the Association of Colleges, said: "Employers' history of paying for their staff training is at best patchy and at worst non-existent - as this report once again demonstrates.
"With the prospect of a national skills crisis ahead, we believe it is time for employers to recognise the demands of the global economy, face up to their responsibilities and invest in the upskilling and retraining of their workforce."
Skills Minister Phil Hope said: "No government has done more to ensure young people do not leave schools without the basic skills.
"Standards in English and maths are at their highest levels ever and all the evidence from key stage results, international comparisons, and Ofsted reports make this clear."
A survey for the National Institute of Adult Continuing Education finds that 77% of workers think doing a job is the best way to improve at it. Some 4,924 UK adults were interviewed.
Meanwhile, a survey of more than 800 employers commissioned for the LSC suggests that the skill most (61%) are looking for is good communication.
This was followed by team-working (58%), self-motivation (41%) and problem-solving (28%).
The survey coincides with Learning at Work Day, part of Adult Learning Week.