Six in 10 think employers cannot be relied on to take responsibility for improving skills, according to a survey commissioned by the Association of Colleges.
Six in 10 people and half of the over 55s, also say they will need to upgrade their skills in the next few years to protect their income and job prospects.
But John Brennan, AoC chief executive, said that while people are recognising the need for more training, colleges are not being given the cash to deliver.
He said: "These figures show that the public has got the message about the importance of improving their skills.
"It is a matter of great concern for us that at the same time as expectations are rising, the Government's funding policy is failing to meet that demand.
"People do not trust their employer to improve their skills. They feel so strongly about this that they believe the Government should fine those companies who fail to train workforces properly."
The employers' organisation, the CBI, blamed schools and colleges for not equipping people for the world of work.
A spokesman said: "Employers take the training of staff extremely seriously and spend pound;23.5 billion a year on it, much of it to make up for the education system failing."
The survey was conducted by ICM Research who interviewed 2,045 people on behalf of the AoC. It showed that the group most concerned about on-the-job training were those in full-time education.
In this group, 77 per cent believe they will need to continue improving their skills, and 79 per cent agree that the Government should fine companies who fail to train their workforce properly.
A Department for Education and Skills spokeswoman said that the Government took training seriously. Its Skills Strategy was introduced to encourage employers to offer the training needed for their business to succeed.