Thanks for all your help, Christine. I found the list of Cranmers and various spellings including Crenmor on the IGI FamilySearch website. There is a marriage of a John Crenmor to Mary Hedley on 21 December 1759 in the parish of All Saints, Newcastle upon Tyne (Batch No. M 004295 (1751-1791) Source Collection No.1068939 - film. John was born on 14 February 1739 and christened on 25 February 1739 at Groat Market Meeting (NC - ?Non-Conformist), Newcastle upon Tyne. Was this a Quaker meeting house? The source for this was Batch No. P 004241 (1726-1836) Souce call No. 0087983, Film. Printout Call No.6905667. John's father however is named as William Cranmer. The Carlisle branch appear to be related in some way to the Newcastle Cranmers, with a Hedley Cranmer, son of a William Cranmer and Jane Leithen (not the same William as mentioned previously as the gap in years is too large) and who was baptised 4 June 1789 in the parish of St. Cuthbert, Carlisle, Cumberland.
Re. the Hedley you mention, is it the surname or the occupation of his father, which is mentioned?
Still trying to unravel a possible connection betgween the Northumberland and Cumberland branches and follow the trail back from 'my' Cranmers, who appear in Antrim, Ireland working in the calico printing industry in Carnmoney, Antrim, after having migrated from England (probably Northumberland or Cumberland) as they were related to a family of calico printers, and there were calico printers in the Carlisle branch. They then went to Scotland (Perthshire, Glasgow and an area of Dunbartonshire close to Glasgow where they worked in calico printing and then linen bleaching. At various times several family members went to live and work in the Manchester area and returned to Perthshire. In a later generation, several daughters married and with their spouses went to work in the Lancashire/Derbyshire area.
It seems possible, that the name of Hedley Cranmer, which occurs subsequently in several generations and branches of the family, originated with the marriage of John Crenmor (Cranmer) to Mary Hedley. What do you think? I've looked back through several generations of Hedley family members, but not knowing Northumberland particularly well, have no idea how close some of the places are to either Newcastle or Hexham.
I've searched the internet for info. about 18th century industries in Northumberland, trying to see if there was any history of calico printing there. No luck, so far. I expect it may mostly have been a cottage industry and handloom weaving would still have been ostly a domestic process when the industrial revolution was in its infancy.