The actual cost of the implementation of Pounds 1,000-a-year tuition fees was revealed this week, as the Scottish institutions were continuing to seek legal clarification on existing legislation.
They fear that thousands of English, Welsh and Northern Irish students will be deterred from applying because, unlike Scottish and other EU students, they will not be exempt from paying for the fourth year of a Scottish degree course.
Technically, non-British European students must be treated as "honorary Scots" and have the final year of a four-year course paid for them. Most Scottish degrees run over four years.
According to the Scottish Office there are about 2,700 EU undergraduates in Scottish universities. At least 350 of these are currently staying on for the final year.
Dr Ronald Crawford, secretary of the Committee of Scottish Higher Education principals, said that the cost of subsidising the EU students would create a "major dent" in the HE budget. He said the Government had so far not offered to help to meet the cost.
He added: "Our greatest concern, however, is that hundreds of British students will be deterred from applying for higher education in Scotland because the perception will be that Scotland is more expensive than elsewhere."
One in five students attending Scottish universities comes from England, Wales or Northern Ireland.