On a serious note here - It is very likely that if you are personally resident in the Republic, and have a UK registered company - unless you structure it carefully (and take professional advice) upi could make the UK company resident in Ireland, and have Irish tax consequences rather than UK.
If you are a sole trader - the business residence will be where you are resident.
Once the residenct position is decided -Then you can decide whether UK of Irish tax rules apply - then you can look further into the matter.