For details of the announcement please see: https://www.gov.uk/
In summary, if a deal is not reached, it is now proposed that EEA citizens arriving in Britain post 29 March 2019, who wish to stay longer than 3 months, will be required to apply for new European Temporary Leave to Remain status, which if granted will be valid for a period of up to 3 years. At the end of that time, a further application under the new skills-based immigration system (commencing in 2021 and still yet to be finalised) would need to be made if the individual wished to continue to remain in the UK.
The new proposals will not affect the rights of EEA citizens already living in the UK prior to 29 March 2019 as they will be able to register under the recently introduced EU Settlement Scheme (Scheme).
The above represents a dramatic and unexpected shift in position from the transitional arrangements as provided for in the draft Withdrawal Agreement. Under that Agreement the position would be that EEA citizens could continue to arrive in the UK post Brexit at any time up until 31 December 2020 and still be able to apply to join the Scheme i.e. an extension of free movement would continue until that time. The latest Home Office announcement totally removes this "grace" period and now, in theory, leaves EEA nationals in the unfortunate position of now only having two months to move to the UK should they wish to be certain of being able to settle under the exiting Scheme.
As mentioned, the above is still only a proposal based on a no deal Brexit and would have to be legislated into law.
Authored by Roxanne Buckley and John Dorney.