If the company does not already have a tax presence in Ireland, and isn't willing to set one up, (unlikely to be worth it for just a single employee), then you can't work as an employee from Ireland for them.
It's possible you could work officially for another company who employ you, and invoice the company you actually work for. I don't know the ins and outs of this but it's a bit complicated. You would effectively be a contractor.
If you live near the border with Northern Ireland, then there are cross-border exemptions that allow you to live in Ireland and work in the UK, and vice versa. But that would be difficult to justify if you're actually living in Cork.
I think there are probably people who do this, and don't tell, and use a friends address in the UK for tax purposes etc. But it's not legal.