However, of the 63% of parents who contribute financially, a fifth are prepared to exhaust all their cash savings to do so, according to the annual survey of student finances by the Association of Investment Companies (AIC).
On average, UK students currently expect their debt on graduation to be over £27,000 (though parents hope it will be nearer £22,000).
Scottish expectations will be lower due to free tuition, and the government has said Scots students studying here have the "best funding package available in the UK", but controversial changes brought in last year have shifted the balance towards loans and away from grants for poorer students. Analyst Lucy Hunter said for young students from households with an income below £25,000 studying in Scotland, the grant loss has been between £890 and £1640 a year.
The AIC survey also found 14% of parents believed their children will find part-time work while at university, but only 8% of new students said they planned to do so as the main way of funding their time at university.
Some 16% of parents said grandparents are helping towards the cost of university, up from 11% in 2011 - at an average of £1907 per year.
The AIC said: "Whilst 17% of students who are planning to go to university say they will live at home to save money during term time, some 44% of parents think it likely their children will live at home to save money, suggesting some awkward conversations at home."
Of parents giving financial support, 55% will use savings, 12% will sell shares and investments, 7% will take out a loan, 6% will downsize the family home to release cash, and 4% will remortgage.
Parents also said they are willing to sacrifice annual holidays (26%), new cars (18%), early retirement (13%), and home improvements (12%) to help their children.
Annabel Brodie-Smith at the AIC said: "As university expenses continue to spiral, reliance has increased on the bank of mum and dad, and now the bank of grandma and grandpa is becoming significant."
She went on: "A saving of £50 per month over 18 years in the average investment company has grown to £26,206, which would be a big help towards university costs. Over the same period, a lump sum of £1000 would have grown to £4020 … investment companies are a useful way to invest for children."
Meanwhile, students in Scotland are being encouraged to get their funding applications in to the Student Awards Agency for Scotland (SAAS) by tomorrow to ensure their money is in place for the start of the new term.
All students are entitled to a loan of up to £4750 for the year, regardless of their parents' income, increasing to £5750 for those from households with a combined income of less than £34,000. These students are also entitled to a bursary, which varies depending on household income.
If applying for a loan of more than £4750, or a bursary, details of household income are needed. This can include documents such as parents' P60s, or if parents are divorced, a solicitor's letter or divorce decree.
All students studying in Scotland must also apply for their tuition fees to be paid by SAAS each academic year; those studying elsewhere can apply for a loan to cover fees. The entire application process can be carried out online.
David Wallace, chief executive of SAAS, said: "We know how important funding is to students, so I'd urge who needs help with the application process to go to our website or call our helpline, rather than putting it off."