There will be no curbs on immigration either from the EU or from outside of it. Jeremy Corbyn (voting record) has stated that the only solution to immigration is the economic improvement of the countries migrants come from and he is therefore unsympathetic to migration controls.
All migrants who ask will be given houses which have their rents and tenancies fixed and from which it is impossible to be evicted.
Landlords who were unlucky enough to be landlords when Labour was in government in the sixties learnt this to their cost. Their tenants could not be evicted even if they never paid rent, never went to work, sublet, or vandalised the property.