Couple of nice little BBC videos here – one showing the cranial remains of Swanscombe (wo)man (a Neanderthal from 400,000 years ago) and another video of the 200,000 year-old Neanderthal remains in the Pontnewydd caves, North Wales which you mention - North Wales being the furthest west they got it seems.
Don’t think there’s evidence of them in Ireland – yet ;-)