A birch Betula. Not sure which species, they're a tricky group which often hybridise. Not Silver Birch Betula pendula (the species perhaps most common in cultivation), the bark and leaf shape isn't quite right.
It seems like B. pendula to me. Here is a link, which I hope works which shows the difference of the two wild types in Ireland. Basically if the twigs are downy, it is B. pubescens. But, of course, that does not preclude other species. (http://www.gardenplansireland.com/forum/about638.html)