Hi thalliday1985,
In moving to the UK, you will become tax resident in the UK. This means your employment with the company in Ireland, will be taxable in the UK and not Ireland.
You would need to arrange for your employer to stop deducting tax in Ireland, so that you can pay the tax in the UK, by completing a self assessment tax return.
We can't advise you what you need to do to notify the Irish tax authorities. If you are resident in the UK, you could apply for a certificate of residence, that you can send to the Irish tax authority.
(
How to apply for a certificate of residence to claim tax relief abroad).
Thank you.