The widow of Inspector Morse actor John Thaw said it was awful students had to leave university with crippling debts.
During a talk with the university's journalism students, Mrs Hancock, who took up the post last year, said: 'I'm appalled that anybody has to pay anything for education, I have to say.
'It's been a belief that I've hung on to all my life and I was appalled when it was changed because I think for young people to have to leave in debt is really awful.
'The economics of running a university I know are very, very hard so you can't be too gung-ho about it because many more young people are going to university now, thank goodness, than did in the old days, so therefore more money is needed to run them.
'But I worry about it. I think education is everybody's right and our future lies in our young people being well educated.'
Labour abolished maintenance grants for poorer students in 1998. By 2006 top-up fees of £3,000 a year were being charged to students.
The average Portsmouth university student now leaves with a debt of £12,403.
Ms Hancock's comments struck a chord with the listening students.
Hannah Clare, 18, a first-year journalism and English literature student, said: 'It was very reassuring to hear our university chancellor talk so passionately about the student fees.
'She was very friendly and answered our questions with great detail.'
But Havant MP David Willetts, the shadow secretary for universities, said free university education wouldn't be possible with so many now going to higher education.
He said: 'It would be nice. But if we want half of school leavers to go to university then the quality of education would suffer without fees as there isn't the public money for all.'
A spokesman for the Department for Innovation, Universities and Skills said the government had increased it funding to universities in real terms by more than 23 per cent since 1997/98.