Amongst the reference points on Census 1861-1901 that link to Low Street are " Barley Stack, The Vicarage, Gas Yard, Police Station, Brewery". There was also reference to "Magistrates" (which I'm struggling to find again!)
As such I was drawn to the junction of Longtown Road and Back/Front Street - see old map already posted.
The Barley Stack no longer a pub (listed building) and is on Carlise Rd, close to the junction with Longtown Rd.