Yes, Irish raiding parties organized by the ancestors of the most powerful early medieval Irish dynasties ravaged the western coast of Britain for nearly a century, between the 4th and 5th centuries. These weren't just pirate raids, they were comparable in size and intensity to the viking raids of the late 8th and early 9th centuries.

They're mostly apocryphal, but the origin stories of the Eoganachta and Ui Neill dynasties both involve military adventures in Britain with the carrying off of massive amounts of slaves and material wealth. Niall Noigiallach ('Of the Nine Hostages'), semi-mythical/historical Irish High King and founder of the Ui Niall dynasty allegedly took his name by accepting the submission of the five Irish provinces, the Scots, the Britons, the Saxons and the Franks. His adventures are sort of confused because they take place in Continental Europe (the Irish had probably forgotten that Britain used to be a Roman colony by the early medieval period and figured that Niall's transgressions against that entity had to have taken place on the Continent), but at least one historical text makes reference to his actions in Britain. Niall was supposedly killed while campaigning in Britain by the king of Leinster's son, which is recorded in the Chronicon Scottorum, an early Irish annal:

AD 411: Niall of the Nine Hostages died, after being wounded by Eochaidh, son of Enna Cennsealach, at the Ictian Sea.

The Ictian Sea was probably what the Irish called the English Channel, so although this historical reference really doesn't tell us much, it confirms that powerful Irish aristocrats were conducting relatively large scale military campaigns in Britain.

The concentration of wealth in the hands of the Irish warrior-aristocracy and the creation of mercenary 'vassal peoples' actually founded the two bases of Irish society that would endure until the 16th century: the clan system and the structure of dynastic kingship. The large influx of slave-labour enabled the development of the warrior-aristocracy, as members of the aristocratic household could divert their energies to martial endeavours rather than agriculture. They formed small, horse-borne strike forces which enabled them to intimidate farmers into providing them with food and finished goods.

The Irish didn't just raid Britain; they also set up shop there. Irish colonies were founded in coastal areas of Wales, Cornwall and Scotland, whose kingdom was essentially an outgrowth of the original Irish colony there (Scotland literally takes its name from the Irish - 'Scotti' was a late Roman term for the inhabitants of Ireland). It's possible that Irish settlement in Britain was only ended by the simultaneous expansion of the Anglo-Saxon kingdoms, although at least one early medieval Welsh dynasty was of Irish descent.

Diarmait mac Máel na mBó is an interesting example here though near the end of your time frame. He was king of Leinster from 1042-1072, a self proclaimed High King of Ireland and he installed his son Murchad as King of Dublin after defeating the irish norse of Dublin in 1052. Then in 1061 he invaded the Isle of Man, which was a norwegian colony at the time, and installed Murchad as 'king of the foriegners'.

He seemed to have a habit of taking in claimaints for english and welsh thrones and backing them with troops, Gruffudd ap Cynan and his father took refuge there after being driven out of Gwynedd by Gruffydd ap Llywelyn and, after Diarmaet's death, it was irish troops from that kingdom that would form the army that retook gwynedd for gruffudd. Ælfgar, Earl of Mercia, did the same thing when exiled in the 1050s and the army that burned hereford and saw him reinstated him to the earldom of mercia included men from ireland as well as wales and possibly norway (the norway thing is debateable, some sources believe there were norwegian princes involved but that seems unlikely given the history of warfare between Diarmait and the irish sea norse colonies, more likely they'll be norwegian troops from the irish colony of the isle of man but it doesn't help that we have two different dates for when this happened: 1053 and 1056). And after the norman invasion, he lent his fleet to Harold Godwinson's sons in their first attempt to overthrow William.

Most of these seem to be mercenaries for a british lord and king but I think there's a very thin line between the irish coming over as allies of that lord and king or as just paid soldiers and it might have been closer to the former than the latter.