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The long building you refer to was undoubtedly the old rope walk or ropery, which is in evidence in maps dating back to at least 1860. You can see it well on this old Ordnance Survey map https://communities.northumberland.gov.uk/005069FS.htm and a nice old photo here https://www.flickr.com/photos/nigeleve/16010579242
You can find more information by visiting the Historic England website and searching ‘Hexham Ropery’ (it was listed Grade II)
Permission was given to demolish it a few years ago, but this was tied into the re-development of the old bus station site, which appears to have ground to a halt.
A general ‘google’ search of Hexham Ropery will give you a lot more information. It’s unclear when the cafe/fish and chip shop was last in use.