The modern language Cumbric is most closely related to is Welsh and it only slightly resembles the other Celtic languages like Breton, Scots Gaelic and of course, Irish Gaelic.

Cumbria was part of what Welsh-speakers and Welsh literature used to call Y Hen Ogledd (the old North). Cumbria itself was the Cumbric-speaking Kingdom of Rheged which existed from the end of Roman Britain until they were absorbed by the Anglo-Saxon kingdom of Northumbria in the 8th century. Cumbric is a geographical term meaning the Old Welsh/Brytonic spoken in Cumbria. The name has the same derivation as Cymry in Welsh, literally "companions" or "countrymen". The place names there are essentially Old Welsh and are one of the only surviving examples of what the Cumbric dialect of Old Welsh looked and sounded like. No other written sources survive, unfortunately.

One of the oldest surviving Welsh poems Y Gododdin was likely composed originally in Cumbric in Cumbria. It describes a battle between the Welsh-speaking Northerners and the Anglo-Saxon community at Cattrick in North Yorkshire. (Spoiler alert: the Welsh lost the north). Only later middle Welsh versions of the poem are known, today. Once part of the kingdom of Northumbria, Old English gradually replaced Cumbric in Cumbria, with the language being lost by 12th Century.

I think Cumbria was more Brythonic. There's traces of the Cumbric strand of Brittonic still present in the Yan tan tethera counting rhyme used by shepherds in northern England around what is now Cumbria. I'm sure there was trade with the nearby Gaels but that the majority wouldn't have spoken it.