The whole story of the nobel "Celts", as a tribe which inhabited the UK and were driven into the Western extremes was invented by the Tudors who had no substantial claim to the English throne, but came from Wales, so invented this whole story about the true inheritors of Britain having been driven into Wales, and now reemerging from Wales
Their propaganda machine was so good people still believe it today. The tribe we call "celts" only ever inhabited the Western fringe of the UK, and dominated the whole island from there, there technology, political and military structures etc were so much more advanced than hours, they set up and upheld rulers to rule the whole of Britain.
So places like Ireland were English long before they were "Celtic" and in fact nobles sent their sons to Ireland to learn proper English there, before they were galic speaking!
And as for were this tribe even "Celtic" - no they weren't, nobody seriously believes that these days. That was a Victorian invention, much like Scottish clan tartan....
Ok, let's unpick this farrago of poorly-understood elements of archeology, language history, Tudor propaganda and modern national identity.
Yes, the extent to which the Iron Age people who lived in these islands should be considered 'Celts' is now disputed. That the languages referred to as 'Celtic languages' existed is not. Old Irish, one of the Goidelic languages, was being written in Ogham inscriptions by the 3rd/4th century, and the earliest Old Irish texts date from around the 8th century. English was first introduced into an Irish-speaking (not 'Gaelic'-speaking) Ireland with the Norman invasion of the 12th century, but was only spoken in the Pale and by the time of the Tudor conquest (which, whatever the Tudors' domestic investment in their Welsh origins, viewed the Irish as politically troublesome savages, rather than 'noble Celts' read Spenser, for heaven's sake!), the Normans had become thoroughly absorbed and even the Pale was predominantly Irish speaking, a situation that remained the case until the 19thc, when English began to predominate over most of the island.
I'd be very interested to see evidence of the trend for English 'nobles' (who? when? why?) sending their offspring to learn 'proper English' in Irish households 'before they were galic [sic] speaking'? When exactly are you thinking of?
And yes, in Ireland the 'Celtic Revival'/ 'Celtic Twilight' became an important element of cultural nationalism in the late 19th c, off the back of antiquarian interest in Old and Middle Irish, and contemporary Irish-language folktales, particularly in the west of Ireland which had been less subject to colonisation -- but the highly distinct culture, liteature and language on which the movement drew for its inspiration was not invented.