A new MORI poll shows that people believe such youngsters face lifelong prejudice, and are more likely to be involved with crime, drugs and booze.
But 81 per cent of people interviewed said they would be happy to employ a care-leaver, and more than half believe that young people enter care because of circumstances beyond their control.
Looked-after children are statistically far more likely to be excluded from school and to perform badly at GCSE level. Only 15 per cent go on to further education, compared to 68 per cent of the general population.
Yet almost half of those surveyed by MORI thought 25 per cent or more of care-leavers made it into post-16 education.
The poll was carried out on behalf of the Prince's Trust and the Camelot Foundation, a charity which helps disadvantaged people to find a fuller role in society. They are funding a three-year, pound;1.15 million mentoring project for care-leavers.
The aim is to to provide 1,300 trained volunteer mentors supporting up to 4,000 young people around the country. Already running in England and Scotland, there are plans t extend the project - now in its second year - to Northern Ireland and Wales.
Yolande Burgin, the Camelot Foundation's charitable project manager, said helping such teenagers into further education was a key part of the mentors' work.
"The mentors work with youngsters for one or two years, to help them through leaving care and moving to independent living. Education - further, higher, further training - is critical. It's how you switch into a successful future rather than drift.
"A lot of young people haven't got the confidence to try college. It's nothing to do with their ability but because of the difficulties many face. The mentors encourage them, and often help them apply - doing some of the stuff our parents did for us."
The MORI survey, of 1,011 adults, also found:
Just over half thought care-leavers face lifelong prejudice.
Young people in care are far more likely to be hooked on booze or drugs, said 42 per cent.
And 45 per cent reckoned they were far more likely to be involved in crime.
81 per cent disagreed with a statement about not wanting a care-leaver working for them.
And more than half felt supportive and sympathetic towards care-leavers.