> there was once a kingdom of Ireland until England had its way

There was, but its king was the King of England (and later of Great Britain), and its parliament was subjugated to the parliament at Westminster, which could veto its acts and legislate directly for Ireland. It saw a brief period of autonomy towards the end of the eighteenth century, when its relationship with Britain became more akin to that between England and Scotland from the Union of the Crowns to the Act of Union; but after the United Irishmen revolt, Britain convinced the Parliament of Ireland, at least partly through bribery of its members, to abolish itself, and Ireland was formally absorbed into the UK.

Before the Kingdom of Ireland was the Lordship of Ireland, which was much the same, but with the King of England as Lord (rather than King) of Ireland, a title granted in 1154 by the first and only English pope, Adrian IV. (Henry VIII had himself declared King of Ireland after his breach with Rome, to quash the belief that the Pope was Ireland's ultimate sovereign.)

Before the Lordship there was a whole mass of kingdoms and sub-kingdoms (including the Kingdom of Dublin mentioned by ptaipale in a sibling to this comment), sometimes united under a High King, the most famous possibly being Brian Boru.

That’s an impressively comprehensive, concise and well-informed history of Ireland with regard to its various kingdoms. I only learned some of this history in the past two years and while I had learned that Henry II had received a papal mandate to conquer Ireland, I hadn’t realised until now that Adrian IV was actually English.

For some odd reason, I was sure there was an independent kingdom but clearly not. I think I've played too much Ck2 to remember my real history now. Thanks for that :)

Well, like I said, there was the High Kingship, but opinion seems to be divided on whether it represented a genuine political union, a confederation, a series of occasional and temporary alliances, a courtesy title for a "first among equals", a claim of supremacy not necessarily accepted by other Irish kings, or all of the above at different times. And at least some of its incumbents, especially the earlier ones, were entirely fictional.

If you're into historical fiction, I can recommend the Saxon Stories by Bernard Cornwell:

https://en.wikipedia.org/wiki/The_Saxon_Stories

I don't know how historically accurate they are, but they're relatively fast paced, fun to read and take place around the time where there were several kingdoms.

And there was also a Kingdom of Dublin, ruled by the Danes.

It lasted from 853 AD to 1171 when the Norman conquest finished it off -- in fact, this is a longer time than what the Acts of Union of England and Scotland have lasted so far.

The Saxons also came from area of modern Denmark, to fill the void left by collapsed Roman Britain, which was occupied by Celtic Britons (and Romans from other parts of the Empire)

And the Normans was originally Danes, Icelanders and Norwegians that settled and integrated into Normandy, France, before crossing the channel...

And I'd dare say, even some "Roman Celts"! The roman influence was long and strong.

There is a sixth century memorial stone in North Wales that uses consular dating: "The stone of ... son of Avitorius. In the time of Justinus the Consul." (Justinus was consul in Constantinople in 540 AD.)

Source: http://www.walesher1974.org/her/groups/GAT/media/GAT_Reports..., p. 121.