The European Union “will never accept” a move by Theresa May to raise tuition fees for EU students after Brexit, the European parliament’s Brexit chief has said.

Guy Verhofstadt said he would write to the prime minister following reports that EU students would be charged full international fees, instead of benefiting from the same rates as UK students as now.

“No way! Students mustn’t be victims of Brexit,” Mr Verhofstadt said. “I will write to PM May saying we will never accept this.”

The Brexit coordinator also said “nothing should change” around the Erasmus programme and added that “British students must be able to continue to study in the EU and European students in the UK, as they do now”.

The European parliament gets a veto over any trade agreements between the EU and other countries, meaning tuition fees could become a bargaining chip in any future trade talks if Mr Verhofstadt follows through on his threat and has support in the legislature.

Domestic tuition fees at English universities are £9,250 a year – and EU students currently pay the same rate. But international tuition fees are completely unregulated and can be considerably higher, ranging from around £10,000 to £38,000 a year for top courses.

Tuition fees are a devolved matter and Scottish students still benefit from free education at Scottish universities. EU students studying in Scotland also currently pay no tuition fees, though English students in Scotland have to pay to study there.

The Independent has seen Mr Verhofstadt’s letter to the prime minister, which expresses “concern in relation to recent media reports indicating that the UK government is considering the possibility of a significant raise in the tuition fees for EU students”.

The letter asks Ms May to “alleviate our concerns by confirming that these reports of drastic fee increases are unfounded” and confirm “that the UK government does not intend to undermine the fruitful reciprocal system that is currently in place”.

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Speaking in Westminster on Monday, Chris Skidmore, the universities minister, said the UK needs to attract “global talent, not just from the EU”.

He added: “We want to make sure we have a system that works for all students across the globe.”

Responding to the reports that higher fees were being considered at the weekend, a Department for Education spokesperson said: “Students from the EU make an important contribution to the universities sector and it is a testament to our system that so many students from abroad choose to come and study here.

“Last year, we announced that students from the European Union starting courses in England in the 2019-20 academic year will continue to be eligible for ‘home fee status’, which means they will be charged the same tuition fees as UK students.