Spain has overtaken France as the top destination for UK students wanting a year abroad, with 4,500 going annually.
But Brexit means they now need visas. And some have waited more than a month for a visa appointment.
Spanish authorities said time was needed for universities and students to adapt to the new system.
They said student visa are a priority for all Spanish Consulates.
But, Universities UK International has written to the Spanish embassy and the Foreign Office, asking if students can apply in Spain.
A UK government spokesperson said visa applications were a matter for Spanish immigration authorities, but added it had raised the issue with the Spanish government.
Ella Perret is due to travel to Madrid next week to spend a year there as part of her law degree.
But she says: “I haven’t booked a flight or accommodation because I don’t know if I’m going.”
Like most students, Ms Perret began the process in June, as the visa documents have to be issued within 90 days of departure.
Now the UK is no longer in the European Union, students wanting to study in Spain have to compile a dossier of documents, including:
a medical certificate
proof of income
a criminal-record check
proof of acceptance at a Spanish university