It is believed that there was a land-bridge connecting the south-east of Ireland to the south of England – this existed before humans arrived in Ireland. I mentioned this previously in the post related to the birth of the Irish Sea – where during the Ice Age there existed a freshwater late before it was finally submerged by the sea.
This great map from Wesley Johnson (pity that he stopped blogging in the prehistoric -html only – period of the internet). Here we can see both the freshwater lake and also the land-bridge to the south.
There is 30% less plants in Ireland’s natural environment in comparison to Britain – but they did get to Ireland, but not all of them.