Scottish and Welsh universities could lose high-achieving applicants to English institutions able to recruit unlimited numbers of AAB students, senior figures in the devolved nations have warned.
Anton Muscatelli, vice-chancellor of the University of Glasgow, said that Scottish universities may use new bursaries to compete for English AAB students.
"We have a good proportion of AAB students at Glasgow. I personally don't want to lose that.
"Because of the importance attached to (achieving AAB) by the English White Paper, we will have to respond," Professor Muscatelli said.
Universities Scotland said that its members "are keen to see cross-border flows of students continue and will bring forward competitive offers on fees and bursaries to ensure they continue to attract high-quality students from across the UK".
Glasgow Caledonian University is introducing a new bursary for rest-of-UK students, which offers ?3,000 to those who exceed their entry requirements. Likewise, Heriot-Watt University will offer a ?3,000 bursary for high-achieving rest-of-UK students.
In the Scottish sector as a whole, 13.6 per cent of students from the UK are English, while in Wales the figure is 41.4 per cent.
Philip Gummett, chief executive of the Higher Education Funding Council for Wales, raised the prospect that changes resulting from the White Paper would draw top-achieving students out of Wales.
"English universities are saying to Welsh AAB students: 'come to us'," he said.
In England, the universities of Kent and Essex have unveiled initiatives to attract high-achieving students, including ?2,000 scholarships for students with three A grades at A level, regardless of family income.
Under the White Paper plans, English universities will lose 8 per cent of their undergraduate student places - a proportion that could rise in future years - to form a pool of 20,000 places that will be allocated to institutions charging average undergraduate tuition fees of less than ?7,500 a year.
However, the 8 per cent deduction will not apply to AAB places, which means that institutions with greater numbers of AAB students will have more security of fee income.
Meanwhile, tuition fees for undergraduates from the rest of the UK have now been set by five Scottish universities, averaging ?6,938 per year, excluding bursaries, over the course of a four-year Scottish degree.
The University of Edinburgh and the University of St Andrews will charge rest-of-UK students ?9,000 a year for four years - a total of ?36,000. Both have pledged to provide bursaries.
Heriot-Watt and the University of Aberdeen will charge ?9,000 for the first three years of a degree, but the fourth year will be free.
Glasgow Caledonian University will charge ?7,000 a year for three years, with the fourth year free, for an average yearly cost of ?5,250.
Undergraduate students from Scotland and the rest of the EU will continue to be exempt from fees at Scottish universities.