Hi, I am also descended from the Carr family via the Forsters.
I know that both the families ended up in Carlisle from Hexham, the Forste’s (farmers), worked their the West landing first in the Longtown /Brampton areas, which they quicky populated and the Carr’s move to the Kendal area and then up to Carlisle when it was rapidly expanding.
I do not know this but we are both distantly related to the Carr biscuit family.Both the Carr’s, (millers and bakers), and for me, via Forsters (banking),families who both occupied work peremises in Castle Street Carlisle.
In 1831, John Dodgson Carr establishse his biscuits in what is now the McVittis factory by the Canal, (located for ease of transportation), sadly, the Forster bank went broke in 1834.
Oddly enough, the reason why I went down this rabbit-hole was because my 2x grear grandfather settled in London around 1826 and married in 1830. one of the witnesses wad William Carr. I assumed that they were either friends or more likely, related. I had no idea that I would find any of this.
I hope this helps you, it would be nice to work with someone as serious about this as I am rather than most on Ancestry who seem to dabble.