In view of the historical ambiguity of the status of Irish nationals in the United Kingdom, Section 2(2) of the Immigration and Social Security Co-ordination (EU Withdrawal) Act 2020 states that Irish Citizens do not need permission to enter or remain in the United Kingdom
Unless : -
They fall into one of three categories warranting exclusion on the grounds of public good.
As there are no restrictions on an Irish nationals stay , they would be eligible to apply for British Citizenship after five years residence in the UK ( or three years where married to a British Citizen) without seeking confirmation of their Immigration status under the UK Immigration Rules.
There is an anomaly that now arises, because Irish Citizens do not require permission to enter or remain as a matter of statute. The Law is phrased in this way specifically: -
“ (1)An Irish citizen does not require leave to enter or remain in the United Kingdom, unless subsection (2), (3) or (4) applies to that citizen.”