Unfortunately their isn’t a process or procedure that is used across the board for photographers or for printing companies to ensure that customers wont have this problem again.
Some photographers including myself and many photographers I know only offer high resolution digital files that include the rights to copy and reproduce them. Photographers or Studios that offer digital files without the copyrights will use a watermark on the images to prevent a quality print being produced. So it is hard to comprehend what the circumstances would be for ASDA’s policy to have a useful affect.
Unfortunately it is unclear why some businesses will print anything you like and others questions your rights, but I would advise my clients to avoid buying their prints from ASDA. I will be putting a copyright release form together for all of my future clients to ensure this doesn’t happen to anyone else and everything runs smoothly from now on.
I would recommend ‘The Print Space’ for high quality printing, they offer an amazing range of paper types and sizes. https://www.theprintspace.co.uk/ . Alternatively you can order your prints with me, just ask for a print price list.