For a small island the UK has many wild areas. Those that spring to mind outside Scotland, would be the parts of Wales that you have mentioned and there are many others,the Black Mountains of Wales come to mind. In England there is Dartmoor, Exemoor, Bodmin Moor, the Peak District, the Lakes, North Yorkshire moors, the Pennines, simply miles of stunning coastal walks and many many more superb walks that abound in the UK. Not all go through wild and hilly crags, that is true, but take the Cotswolds for example there is stunning scenery, history by the boat load and you are never far from a watering hole! Sorry Ireland I don't know you well enough to suggest places, but you have magnificent scenery and no doubt fine walks too.