UK Government's figures show that 122,000 EU citizens left the UK in 1Q2017.

In a 13 September article in The Times (London) Minister of State for Immigration Brandon Lewis said (excerpt):

"Since the referendum, the Prime Minister, the Home Secretary and I have been clear that we want EU citizens in the UK to stay and have made protecting their rights a top priority.

That is why in June the government outlined its offer to do just that. We confirmed that no-one living here lawfully will be asked to leave when we exit the EU and they will have a period to make an application to remain here. We want you to stay.

We have also made clear that EU citizens living here before the yet to be agreed cut-off date who get settled status will be treated as if they are UK nationals for education, healthcare, benefits, pensions and social housing. Our objective is that EU citizens living here should be able to continue their lives as before."

However: the govt's plan to cut net migration to 100,000 a year remains operative. And any efforts to keep EU migrants in the UK may be contingent upon similar guarantees for UK citizens living in the EU.

Like everything else connected to Brexit, the eventual outcome will likely depend on which party will suffer most. And the EU has a big advantage in that contest.