I´m an irish student currently doing a PhD in the UK and I have a full studentship. Your options are to either apply for PhD studentship which is open to anyone and will include a stipend. Alternatively you can arrange your own funding from places like IRCSET or marie curie and then contact a Supervisor in your area to ask them to come up with a project for you. PhD students are classed as either EU or international and as you are irish then you are EU and therefore are entitled pretty much to everything a UK student gets.