United Kingdom - Passport & Nationality - Irish Citizenship from Parent (Indefinite Transmission)
If you were born outside Ireland to an Irish citizen (either a mother or father) who were themselves born outside of Ireland, then you will have a claim to Irish Nationality if their Irish Nationality was granted before your birth. This concept is known as "Indefinite Transmission", because Irish nationality could be passed down indefinitely (to children, grandchildren and grandchildren), irrespective of where they are born.
Irish nationality can ONLY pass down by descent if the birth is legitimate.
Finally, an Irish passport will allow you to live and work in the UK. This right pre-dates the UK's entry into the EU, and is therefore not affected by the UK's recent exit from the UK.