QM as a matter of law, Wales has been deemed to be included in England since the C14 and a reference to England includes Wales.So that's one element disposed of. Don't remember whether Ireland before independence was regarded as separate, but I suspect not. If it wasn't, then including the northern province in the title is, and was, strictly superfluous but may have been done consequent upon the rest of the island becoming independent, to remind everyone that we kept this one bit, if only as a province.
So the answer is to call the whole country 'England', as was common practice until about 1930 here and still is in the USA; I have an American book of great golf courses of 'England' which includes Muirfield, St Andrews and the main course at Troon. Or we could call it Britain, allowing for the fact that North Britain or, as some call it, 'Scotland', was no longer a part.