Disagreements in the UK cabinet over the future of EU migrants is just one of many divisions within government and society at large over the kind of Brexit deal they want, Dr. Catherine Barnard told Radio Sputnik.

The free movement of EU citizens to the UK will end in March 2019, after which these European citizens will be subject to a registration system, a spokesman for British Prime Minister Theresa May confirmed on Monday.

Some members of the UK government, including Chancellor Philip Hammond and Home Secretary Amber Rudd, who both wanted to remain in the EU, back the idea of transitional arrangements after Brexit which might allow EU migration to continue under a registration scheme.

There have been media reports of a rift in the cabinet over the issue of extending free movement. Trade Minister Liam Fox, a prominent Brexit campaigner, told the Sunday Times on July 29, "If there have been discussions on that, I have not been party to them."

"We made it clear that control of our own borders was one of the elements we wanted in the referendum, and unregulated free movement would seem to me not to keep faith with that decision," Fox said.

There are 3.2 million EU migrants currently living in the UK. Those who have been in the UK for five years prior to March 2019 will have the right to apply for "settled status," while other EU migrants who are on track to do will be able to apply post-Brexit, Dr. Catherine Barnard, Professor of European Union Law at the University of Cambridge, told Radio Sputnik.

"What's much less clear is what's going to happen to people who arrive after Brexit day, after March 29th 2019. Are they going to be subject to the full force of UK immigration law, which is pretty demanding? It requires a visa, and a contribution to the health service, too."

"Or, as Chancellor of the Exchequer Philip Hammond is suggesting, there might be some kind of transitional arrangements which soften the full force of the application of UK immigration law."

Family reunification for EU migrants could become more difficult after Brexit, because UK immigration laws are stricter on the issue than the EU.

"If they've got family members, for example from Russia, who want to join them in the UK, under EU rules if they move from France to the UK it's very easy to bring in family members but under UK immigration law it's much, much harder to bring in family members who come from other countries so that may well be a challenge for them."

Campaigners for Brexit say that leaving the EU will improve wages for UK nationals, because the constant supply of EU migrants is keeping wages suppressed. Those who campaigned to remain point out that EU nationals are vital to many sectors of the economy.

"For example, nearly 50 percent of people working in the fruit and vegetable processing sector are EU nationals; nearly 50 percent who work in meat processing are also EU nationals and just over a third of those working in fish processing are EU nationals. So, if you think about it in those terms, where are you going to get all of the UK nationals to replace the EU nationals once they've gone?" Barnard asked.

It is difficult to predict the kind of relationship that will develop between the UK and EU after Brexit, since many people in the UK government and in society as a whole disagree about the issue.

"There is goodwill for the UK to retain some sort of close relationship with the EU, but at the moment there is really quite a major fight going on within the cabinet and also within the country about precisely what that relationship will look like. At the moment, we're told it's going to be a deep and special partnership but quite what form it will take, bearing in mind the many difficulties involved, for example what to do about the border with Northern Ireland, all of that is going to be very difficult to work through and it will take years to work through. It certainly won't all be done and dusted by March 29 2019."