As a former compositor and later desk top publisher (how things quickly changed in the 80's) in a career ran from 1958 to 2005, I can tell you that Chorlton & Knowles of Manchester began in the 1800's and was still going strong at least until the 70's (and maybe even later). I think the Moseley Street address was just an office where customer instructions were received and Newton Mill was the actual works. Like many printers in that era, they had a secondary name. In their case it was The Mayfield Press, which suggests they were in the Mayfield area close to London Road Railway Station (now Piccadilly).
I suppose that it is just possible that the Knowles involved with Ramshaw had some connection with the C & K company, but I doubt it.