Wasn't "The Shirt Factory" in the council (BUDC) yard? I can remember the outpouring of girls from there at the end of their shift. It was always a place anyone industrious could get employment. The phrase "she works (worked) at the shirt factory" did have a tiny bit of social stigma in those days, though. It implied that the person might have done better at school. Having said that, it probably paid a lot better than shopworker or clerical jobs. The Rag Trade on TV epitomised this type of work. Work which was steadily eroded by the waves of imports from overseas "sweat shops", but don't get me started on so-called "globalism"!
I recall they had a problem with asbestos roofing in the BUDC yard, and some poor worker being killed when the roof didn't support their weight. This might jog someone's memory on the place.
I can also remember going into the Barrington establishment to deliver or attend to something, or maybe to seek someone out. At this point in time, I can't remember why I was there, though I have a brief mental image of the offices but not the work floor. It was, I think, a conversion and not a purpose-built factory.
Update: Ah, yes, that's it above. Should have scrolled up! Just pointing out the social attitudes (snobbery) of the era, and no downers on the industrious salt-of-the earth people that worked there. A lot of that lingers on in the present day, when the thoroughly brainwashed ex-uni types regard themselves as socially superior and have a right to do everyone's thinking for them!