I doubt if the Sleekurn edition would cover Front Street, West End, Alan. I don't have any of Stephen B Martin's books but I have several by Evan Martin - including the one above, posted by Vic. Evan Martin uses the same photo of 'Baptists Yard' accompanied by almost the same text. Unfortunately he doesn't disclose the source of the photo or the information in the text. He does say that the "The Baptist Yard" contained " Bedlington's first Post Office and in 1858 the telegraph system was installed there." (page 99).
I find it somewhat strange that just 2 years after such an investment, the Post Office would move to new premises nearer the Market Place as shown on the 1860 map. It's also worth remembering that maps aren't created overnight. They take several years of survey work before being published, so the location of the PO shown on that map may well have been surveyed prior to 1860. I have to admit that I have wondered if that really is Baptist Yard and if the PO was ever located there.