Immigration remains a daunting policy concern as the United Kingdom tries to envision a future outside of the European Union. But hopes that Britain and the EU can reach a deal addressing the nation's migrant population could be in vain, according to a leading academic.

For one, "no conceivable Brexit deal will involve expelling" Eastern Europeans currently residing in the U.K., said Paul Collier, professor of economics and public policy at the University of Oxford.

Many are keeping an eye on how Prime Minister Theresa May handles the issue in upcoming rounds of Brexit negotiations. May has pledged to "re-take control of the U.K.'s borders," which includes measures like implementing a migrant registration system.

Her hands could be tied, however, when it comes to handling the millions of non-citizens already living and working in the country.