I have just seen this thread and am surprised that it has not been answered. I cannot volunteer as I live away rom Acc and the next few weeks are spoken for. I suggest that you drop a line to
Accrington.library@lancashire.gov.uk and ask to be sent photos or a photo copy of the relevant pages on Mike Rothwell's book on Hyndburn's Industrial Heritage. This company's premises were in Dowry St. Latterly, their products were called 'New Era' Another Whittaker firm in the town were brickmakers. Another
made 'Pioneer' mangles. Another made sewerage-processing products.
I cannot help with the Matthews patent.
I have never seen the Whittaker archive. By now it may have been transferred to the Lancashire Archives. These are searchable on-line using the National Archives website. It will only give you a reference number.