As per IMDB:
“Daniel Michael Blake Day-Lewis was born in London, England, the second child of Cecil Day-Lewis (aka Nicholas Blake) (Poet Laureate of England) and his second wife, Jill Balcon. His maternal grandfather was Sir Michael Balcon, an important figure in the history of British cinema, head of the famous Ealing Studios. His older sister, Tamasin Day-Lewis, is a documentary filmmaker. Daniel was educated at Sevenoaks School in Kent, which he despised, and the more progressive Bedales in Petersfield, which he adored. He studied acting at the Bristol Old Vic School. Daniel made his film debut in Sunday Bloody Sunday (1971), but then acted on stage with the Bristol Old Vic and Royal Shakespeare Companies and did not appear on screen again until 1982, when he landed his first adult role, a bit part in Gandhi (1982). He also appeared on British TV that year in “Frost in May” (1982) and How Many Miles to Babylon? (1982) (TV). Notable theatrical performances include Another Country (1982-83), Dracula (1984), and The Futurists (1986)”
His father C. Day-Lewis was the Poet Laureate not of "England" but of the United Kingdom, of which Northern Ireland is a part. C. Day-Lewis came from an old Protestant Ascendancy family in Ireland.
Daniel Day-Lewis identifies as Irish.