Are you employed as a PAYE employee of an Irish employer? That's what it sounds like.
HMRC will expect you to pay tax on work that you do in the UK. Your Irish employer would typically either pay you for UK based work from its UK branch or set up a UK branch if it doesn't have one (they may be reluctant to do this for one employee) or use an outsourced payroll solution like IPAYE.
Unfortunately this can all prove a lot more painful than what seemed like an easy decision to let you work at home a couple of days per week.
If you can sort out being paid separately in Ireland and the UK, then there are advantages in getting two sets of personal allowances and lower rate Income Tax bands.
None of this is Gospel, just my understanding from having moved from UK to Ireland some years back and looking at various models that might have worked.