The rhetoric from EU leaders has been consistently stark; if the UK wants to stay in the single market the free movement of people is not up for negotiation. EU leaders are deeply concerned that if they make concessions for the UK, other Eurosceptic member states will demand their own limits on immigration. This would surely lead to the unravelling of the EU as we know it.
From the UK perspective, the ability to place controls on immigration was the single biggest reason for the Leave vote. It would be political suicide for the UK negotiators not to secure some limitations on immigration.
The upshot of these seemingly immoveable positions is that the UK is almost certainly going to have to come out of the single market (a so-called “Hard Brexit”) and curb EU immigration. Many employers have already reached this conclusion and are planning for the impact on their businesses.