Some initial investigation: For those interested the API for requesting image tiles is listed here: https://iiif.io/api/image/3.0/#4-image-requests
The original request URL for image 103313042 is https://map-view.nls.uk/iiif/2/10331%2F103313042/12288,6144,2048,2048/512,/0/default.jpg. The four comma separated values are x, y, width, height values for the tile region and the '512' is the tile size.
You can get the 'full' image by replacing the four region values with 'full': https://map-view.nls.uk/iiif/2/10331%2F103313042/full/617,/0/default.jpg however it is limited by a maximum size of 617 for some reason.
If you can get the image dimensions, this seems much more automatable.