Thanks for your reply.
I don't understand what you mean about the solution offered by the agency and me becoming the employer and employee? Why would I be both?
The alternative is that I would need to also register another company in Ireland with an Irish accountant to pay tax as a Ltd company there?
Im unsure if I am a subcontractor by definition. I invoice the agency that I have the contract with on a monthly basis who then invoice another agency who manage all the contractors for the company that I actually work for. Does this make me a subcontractor? If so the link you sent me is very interesting.