yourworstnightmare
Why? England, after the expulsion of the Viking kings was a rich and powerful state, and then again after the 2nd Viking invasion under Canute. It had some internal divisions which tended to make external power projection a problem despite it's fairly high level of centralisation. However it never, as far as I'm aware attack Ireland nor anyone else except Scotland and Wales where there were continued border disputes. Ireland was actually a fairly friendly neighbour which often supplied trade and a place of exile for displaced English.
The immediate problem was the Norman system of sending younger sons out to make their own future, generally looking to conquer and rule new lands. This made them both expansionist and very destructive of the existing populations and power structures.
Steve
The one documented occasion when the Irish and Anglo-Saxon kingdoms fought was the attack upon the Kingdom of Brega by King Ecgfrith of Northumbria circa 682AD. However this occurred around the same time as hostilities broke out between the Northumbrians and the Pictish kingdoms, making it likely that the there was some element of collusion between the Irish and Picts for King Ecgfrith to strike westwards against Ireland instead of northwards what is now Scotland.
Why wouldn't an Anglo-Saxon England invade Ireland? Sure it may take longer than IOTL, but an England, which gets it's act together and/or has an expansionist ruler, could very well end up in seeing Ireland as a target for expansion.
And who's to say that second (or third etc.) sons in a surviving Anglo Saxon England wouldn't try to do the same?
With England not controlled by the Normans, you butterfly away their expansionist policies. It wasn't the English who initially fought overseas wars to reconquer the Holy land or retake Sicily, but the Normans. With the one exception I mentioned above, the Anglo-Saxons didn't actually fight a war against any people overseas until they were absorbed into King Canute's Danish kingdom, and even then this basically took the form of English levies being raised to fight in internal struggles within this kingdom over the succession of the Danish crown.
Without the fatal combination of Norman expansionism and Papal support, it would be fairly difficult to imagine the circumstances under which an English King would want to seize an island that lacks any usable resources and is at the time mostly bogland or forests with the exception of the southeastern coastline.