From memory, Ackroyds shirt factory was through an arch where the Bedlington Urban District Council offices were. It was through the arch and down a bit on the left. As it was a long time ago and I haven't been near Bedlington for years, the arch in question (with offices above) was on the left going down the Front Street from the Red Lion towards the turning down to Bedlington Station. It was on the opposite side of the Front Street to the library which had Abbs milkman behind the library. I know it is an old thread but thought it may still be of interest.
Further down past the turning for Bedlington Station, going towards Bebside on the left was the Bedlington Glove Company run by Mr and Mrs Mautner, I think the Manager was called Mr Sharman. They made gloves for Marks & Spencer among other companies.