The wealthiest students are going to university in England for the lowest cost, by paying their tuition fees up front, say researchers.
About 10% of students are not taking out loans and so avoid interest rates of 6.3% paid by other students, says the Intergenerational Foundation.
The think tank says it "makes a mockery" of claims that the fees system is fair for poorer students.
The government says that its review of fees will ensure value for money.
"Wealthier families have realised that they can give their children a get-out-of-jail-free-card by helping them to escape sky-high interest rates and a 30-year loan that could be sold off to the private sector in the future," said report author, Rakib Ehsan.
'Making a mockery'
About 10% of undergraduates from the UK are self-funding, says the analysis of official data for 2016-17 - with higher than average rates at some Russell Group universities.
Among full-time students, there are 20% self-funding their fees at King's College London and 16% at Oxford and Cambridge.
University College London, Imperial and LSE are all above average, at around 14%.
This excludes overseas students, or people who might have fees paid for them by job-related support or through scholarships and bursaries.
The researchers say that universities with higher proportions of self-funding students are often those with a higher proportion of students from private school - suggesting that their families might be continuing to pay for university.
For those who can afford it, there are significant savings.
Interest charges begin to build up as soon as a student begins at university - and about £6,000 can be owed before a student even graduates.
Those paying up front will leave not owing this money - and they will not be part of the repayment scheme paying back loans over 30 years.
This will give self-funders a "serious economic advantage" when they leave university, say researchers.
Reducing interest rates
"This analysis makes a mockery of claims that the current system is progressive, since the wealthiest kids are not even in the system," said Angus Hanton of the think tank.
"The government should treat all students fairly and that means reducing the interest rates charged while at university, reducing fees, reintroducing maintenance grants, and lowering the repayment rate," he said.
Shakira Martin, president of the National Union of Students, says it means that wealthy students can avoid debt and high interest rates, while too many poorer students are struggling "to make ends meet".
"The government's claims that the higher education sector is a level playing field are nonsense, and the scrapping of maintenance grants means that in fact they've squarely placed the extra burden on the poorest in our society," she said.
Gordon Marsden, Labour's shadow minister for higher education, said the report showed that the combination of "eye-watering tuition fees and huge interest payments is unfair and unsustainable".
"The fact that the wealthiest students can avoid the thousands of pounds of interest paid by their less fortunate peers exposes a fundamental injustice at the heart of the system."
The government has commissioned a review of student finance in England, with suggestions that it could lower the headline figure for tuition fees.
A Department for Education spokeswoman said the review would be "considering how best to provide value for money, both for students and taxpayers".
She said the loan system was progressive in how repayments were "based on income after graduation, not on the amount borrowed" and that it enabled all students to have funds for studying.
"The student finance system removes financial barriers for those hoping to study but who are unable to self-fund," said the DfE spokeswoman.
"Unlike commercial alternatives, student loans are available to all eligible students, regardless of background or financial history."