The Common Travel Area (CTA) is a long-standing arrangement between the UK, the Crown Dependencies (Bailiwick of Jersey, Bailiwick of Guernsey and the Isle of Man) and Ireland that pre-dates both British and Irish membership of the EU and is not dependent on it.
Under the CTA, British and Irish citizens can move freely and reside in either jurisdiction and enjoy associated rights and privileges, including the right to work, study and vote in certain elections, as well as to access social welfare benefits and health services.
Therefore although Ireland is still a member of the EU if you are an Irish citizen with a valid Irish passport and a UK national insurance number you don't need to demonstrate your right to work in the UK with any additional documents other than your photo Passport ID.
Most production companies prefer passport photo ID as proof of right to work in the UK. To do this you will need your National Insurance number and Date of Birth handy. Upload Passport