I'll go out on a slight limb and assume you mean pre-1172 Ireland, preceeding the Cambro-Norman invasion. The answer is yes, of a sort. The east coast of Ireland in particular was part of an extensive and lucrative early medieval trade network from the late 9th Century onwards that stretched from the West of England all the way to Iceland and the Baltic (and from there joining a wider network via Russia to Constantinople and then the Silk Road to China). The key hubs of this network are the Hiberno-Norse settlements around the Irish Sea such as Dublin, Wexford and Waterford. These ports establish a lucrative trade primarily with the English ports of Chester and Bristol, trading in slaves, cattle, metalwork, wool and cloth, ores, precious metals, and highly-valued English coinage. Such was the relationship that when Dairmait mach Murchada was deposed as High King of Ireland in 1169, he first took refuge in Bristol, and much of the cost of the Cambro-Norman expedition was financed by Bristol merchants.

There is also prior history of less benevolent interaction. Scots and Gaels raided much of Britain following the Roman withdrawal in 410, and there is even some isolated evidence of settlement, such as a hearth and huts found at Eddisbury hill fort in Cheshire.