Those who were citizens of Eire on 1 January 1949 could opt to remain a British subject under Section 4(2) of the British Nationality Act 1948. Such people continue to have that right under the British Nationality Act 1981.
For this purpose, “citizens of Eire” were defined by the Irish Nationality and Citizenship Act 1935 and the Irish Nationality and Citizenship (Amendment) Act 1937.
Those who have no claim to British subject status would need to naturalise, in the same way as other foreign nationals, in order to become British citizens. For this purpose, the term “Irish citizen” would refer to those recognised by the Irish Government under their current legislation as being their nationals. When applying for citizenship, this would normally be demonstrated by possession of an Irish passport.