Immigration enforcement officials are now set to embark on issuing EU citizens who live in the UK a 28-day warning to apply to enable them stay in the country.
However the Home Office will give people an indefinite period to complete an application for settled status if they have a reasonable excuse for delay.
There is a week to go until the deadline for applications.
At least 5.6 million European Economic Area (EEA) citizens and their dependents have applied for settled status.
But there are around 400,000 cases outstanding, and the government’s helpline is receiving thousands of calls a day.
After the 2016 Brexit referendum, which took place precisely five years ago, settled status was introduced for citizens of the EU and EEA living in the UK.
It allows them to retain the same rights of residence, travel, employment and access to healthcare and benefits.
The countries whose nationals have made the highest numbers of applications are Poland (975,000) and Romania (918,000).
Immigration minister Kevin Foster said anyone whose application was not concluded by next week’s deadline would not lose out, as their rights were protected in law.
He added that immigration enforcement officials would begin issuing 28-day notices to people, advising them to apply for settled status.
Migrants’ groups had voiced concern that children would be among those who had not applied.